/* $RCSfile$ * $Author: egonw $ * $Date: 2005-11-10 09:52:44 -0600 (Thu, 10 Nov 2005) $ * $Revision: 4255 $ * * Copyright (C) 2003-2005 Miguel, Jmol Development, www.jmol.org * * Contact: jmol-developers@lists.sf.net * * This library is free software; you can redistribute it and/or * modify it under the terms of the GNU Lesser General Public * License as published by the Free Software Foundation; either * version 2.1 of the License, or (at your option) any later version. * * This library is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * Lesser General Public License for more details. * * You should have received a copy of the GNU Lesser General Public * License along with this library; if not, write to the Free Software * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. */ package org.jmol.symmetry; import java.util.Arrays; import java.util.Hashtable; import java.util.Map; import org.jmol.api.SymmetryInterface; import org.jmol.symmetry.HallInfo.HallReceiver; import org.jmol.util.Logger; import org.jmol.util.SimpleUnitCell; import org.jmol.viewer.JC; import org.jmol.viewer.Viewer; import javajs.util.AU; import javajs.util.Lst; import javajs.util.M4; import javajs.util.P3; import javajs.util.PT; import javajs.util.SB; /** * * A general class to deal with Hermann-Mauguin or Hall names * * Bob Hanson 9/2006 * * references: International Tables for Crystallography Vol. A. (2002) * * http://www.iucr.org/iucr-top/cif/cifdic_html/1/cif_core.dic/Ispace_group_symop_operation_xyz.html * http://www.iucr.org/iucr-top/cif/cifdic_html/1/cif_core.dic/Isymmetry_equiv_pos_as_xyz.html * * Hall symbols: * * https://cci.lbl.gov/sginfo/hall_symbols.html * * and * * https://cci.lbl.gov/cctbx/explore_symmetry.html * * (-)L [N_A^T_1] [N_A^T_2] ... [N_A^T_P] V(Nx Ny Nz) * * lattice types S and T are not supported here * * data table is from Syd Hall, private email, 9/4/2006, * amended using * to indicate nonstandard H-M symbols or full names * * amended 2024.03.24 to add several ITA settings; full set of ITA settings are now encoded. * * NEVER ACCESS THESE METHODS DIRECTLY! ONLY THROUGH CLASS Symmetry * * * */ public class SpaceGroup implements Cloneable, HallReceiver { protected String specialPrefix = ""; private static final String NEW_HALL_GROUP = "0;--;--;0;--;--;"; protected static final String NEW_NO_HALL_GROUP = "0;--;--;0;--;--;--"; private static final String SG_NONE = "--"; static final String NO_NAME = "-- [--]"; // don't know if this is possible private final static int SG_ITA = -2; public int groupType = TYPE_SPACE; public SymmetryOperation[] matrixOperations; SymmetryOperation[] finalOperations; SymmetryOperation[] allOperations; Map xyzList; char uniqueAxis = '\0'; char axisChoice = '\0'; //int cellChoice; //int originChoice; protected String itaNumber; // "3" String jmolId; // "3:a" int operationCount; int latticeOp = -1; boolean isBio; char latticeType = 'P'; // P A B C I F String itaTransform; /** * index in cleg_settings.tab; "-" if in Jmol's list but not at ITA -- 152:_2 and 154:_2 */ protected String itaIndex; /** * number of dimesions -- 2 (plane, frieze) or 3 (layer, rod, space) */ protected int nDim = 3; protected int periodicity = 0x7; // abc private String clegId, canonicalCLEG; private int index; private int referenceIndex = -1; public boolean isSSG; private String name = "unknown!"; private String hallSymbol; private String hallSymbolAlt; private String crystalClass; //schoenfliesSymbol; private String hmSymbol; private String jmolIdExt; // "a" in "3:a" private HallInfo hallInfo; private int latticeParameter; private int modDim; private boolean doNormalize = true; private Object info; private Integer nHallOperators; private String hmSymbolFull; private String hmSymbolExt; private String hmSymbolAbbr; private String hmSymbolAlternative; private String hmSymbolAbbrShort; private char ambiguityType = '\0'; private SpaceGroup setFrom(SpaceGroup sg, boolean isITA) { if (isITA) { setName(sg.itaNumber.equals("0") ? clegId : "HM:" + sg.hmSymbolFull + " #" + sg.clegId); referenceIndex = SG_ITA; // prevents replacement in finalizeOperations } else { setName(sg.getName()); referenceIndex = sg.index; } setClegId(sg.getClegId()); itaIndex = sg.itaIndex; crystalClass = sg.crystalClass; hallSymbol = sg.hallSymbol; hmSymbol = sg.hmSymbol; hmSymbolAbbr = sg.hmSymbolAbbr; hmSymbolAbbrShort = sg.hmSymbolAbbrShort; hmSymbolAlternative = sg.hmSymbolAlternative; hmSymbolExt = sg.hmSymbolExt; hmSymbolFull = sg.hmSymbolFull; itaNumber = sg.itaNumber; itaTransform = sg.itaTransform; jmolId = null; jmolIdExt = null; latticeType = sg.latticeType; specialPrefix = sg.specialPrefix; periodicity = sg.periodicity; groupType = sg.groupType; strName = displayName = null; return this; } static SpaceGroup getNull(boolean doInit, boolean doNormalize, boolean doFinalize) { // getSpaceGroups(); SpaceGroup sg = new SpaceGroup(-1, null, doInit); sg.doNormalize = doNormalize; if (doFinalize) sg.setFinalOperations(); return sg; } protected SpaceGroup(int index, String strData, boolean doInit) { ++sgIndex; // increment even if not using if (index < 0) index = sgIndex; this.index = index; init(doInit && strData == null); if (doInit && strData != null) buildSelf(strData); } private void init(boolean addXYZ) { xyzList = new Hashtable(); operationCount = 0; if (addXYZ) addSymmetry("x,y,z", 0, false); } public static SpaceGroup createSpaceGroup(int desiredSpaceGroupIndex, String name, Object data, int modDim) { SpaceGroup sg = null; if (desiredSpaceGroupIndex >= 0) { sg = SG[desiredSpaceGroupIndex]; } else { if (data instanceof Lst) sg = createSGFromList(name, (Lst) data); else sg = determineSpaceGroupNA(name, (float[]) data); if (sg == null) sg = createSpaceGroupN(modDim <= 0 ? name: "x1,x2,x3,x4,x5,x6,x7,x8,x9".substring(0, modDim * 3 + 8), true); } if (sg != null) sg.generateAllOperators(null); return sg; } // SpaceGroup cloneInfoTo(SpaceGroup sg0) { // try { // SpaceGroup sg = (SpaceGroup) clone(); // sg.matrixOperations = sg0.matrixOperations; // sg.finalOperations = sg0.finalOperations; // sg.xyzList = sg0.xyzList; // return sg; // } catch (CloneNotSupportedException e) { // return null; // } // } public String getItaIndex() { return (itaIndex != null && !SG_NONE.equals(itaIndex) ? itaIndex : !"0".equals(itaNumber) ? itaNumber : !SG_NONE.equals(hallSymbol) ? "[" + hallSymbol + "]" : "?"); } public int getIndex() { return (referenceIndex >= 0 ? referenceIndex : index); } public void setClegId(String cleg) { clegId = cleg; canonicalCLEG = canonicalizeCleg(cleg); } public String getClegId() { return clegId; } /** * * @param name * @param data Lst or Lst * @return a new SpaceGroup if successful or null */ private static SpaceGroup createSGFromList(String name, Lst data) { // try unconventional Hall symbol SpaceGroup sg = new SpaceGroup(-1, NEW_NO_HALL_GROUP, true); sg.doNormalize = false; sg.setName(name); int n = data.size(); for (int i = 0; i < n; i++) { Object operation = data.get(i); if (operation instanceof SymmetryOperation) { SymmetryOperation op = (SymmetryOperation) operation; int iop = sg.addOp(op, op.xyz, false); sg.matrixOperations[iop].setTimeReversal(op.timeReversal); } else { sg.addSymmetrySM("xyz matrix:" + operation, (M4) operation); } } SpaceGroup sgn = sg.getReferenceSpaceGroup(); if (sgn != null) sg = sgn; return sg; } /** * * @param xyz * @param opId generally 0; -1 for subsystems * @param allowScaling generally false; true for subsystems * @return index */ public int addSymmetry(String xyz, int opId, boolean allowScaling) { xyz = xyz.toLowerCase(); return (xyz.indexOf("[[") < 0 && xyz.indexOf("x4") < 0 && xyz.indexOf(";") < 0 && (xyz.indexOf("x") < 0 || xyz.indexOf("y") < 0 || xyz.indexOf("z") < 0) ? -1 : addOperation(xyz, opId, allowScaling)); } void setFinalOperations() { setFinalOperationsForAtoms(3, null, 0, 0, false); } void setFinalOperationsForAtoms(int dim, P3[] atoms, int atomIndex, int count, boolean doNormalize) { //from AtomSetCollection.applySymmetry only if (hallInfo == null && latticeParameter != 0) { HallInfo h = new HallInfo( HallInfo.getHallLatticeEquivalent(latticeParameter)); generateAllOperators(h); //doNormalize = false; // why this here? } finalOperations = null; isBio = (name.indexOf("bio") >= 0); if (!isBio && index >= SG.length && name.indexOf("SSG:") < 0 && name.indexOf("[subsystem") < 0) { SpaceGroup sg = getReferenceSpaceGroup(); if (sg != null && sg != this) { setFrom(sg, false); } } if (operationCount == 0) addOperation("x,y,z", 1, false); finalOperations = new SymmetryOperation[operationCount]; SymmetryOperation op = null; boolean doOffset = (doNormalize && count > 0 && atoms != null); if (doOffset) { // we must apply this first to "x,y,z" JUST IN CASE the // model center itself is out of bounds, because we want // NO operation for "x,y,z". This requires REDEFINING ATOM LOCATIONS op = finalOperations[0] = new SymmetryOperation(matrixOperations[0], 0, true); if (op.sigma == null) SymmetryOperation.normalizeOperationToCentroid(dim, op, atoms, atomIndex, count); P3 atom = atoms[atomIndex]; P3 c = P3.newP(atom); op.rotTrans(c); if (c.distance(atom) > 0.0001f) { // not cartesian, but this is OK here for (int i = 0; i < count; i++) { atom = atoms[atomIndex + i]; c.setT(atom); op.rotTrans(c); atom.setT(c); } } if (!doNormalize) op = null; } for (int i = 0; i < operationCount; i++) { // not necessary to duplicate first operation if we have it already if (i > 0 || op == null) { op = finalOperations[i] = new SymmetryOperation(matrixOperations[i], 0, doNormalize); } if (doOffset && op.sigma == null) { SymmetryOperation.normalizeOperationToCentroid(dim, op, atoms, atomIndex, count); } op.getCentering(); } } private static HallInfo newHallInfo(String hallSymbol) { if (hallSymbol.startsWith("Hall:")) hallSymbol = hallSymbol.substring(5).trim(); return new HallInfo(hallSymbol); } int getOperationCount() { if (finalOperations == null) setFinalOperations(); return finalOperations.length; } M4 getOperation(int i) { return finalOperations[i]; } /** * This call retrieves the count of all operations, including operations that * arise from adding lattice translations. * * @return allOperations.length */ int getAdditionalOperationsCount() { if (finalOperations == null) setFinalOperations(); if (allOperations == null) { allOperations = SymmetryOperation.getAdditionalOperations(finalOperations, periodicity); } return allOperations.length - getOperationCount(); } M4[] getAdditionalOperations() { getAdditionalOperationsCount(); return allOperations; } M4 getAllOperation(int i) { return allOperations[i]; } String getXyz(int i, boolean doNormalize) { return (finalOperations == null ? matrixOperations[i].getXyz(doNormalize) : finalOperations[i].getXyz(doNormalize)); } public static SpaceGroup findSpaceGroupFromXYZ(String xyzList) { SpaceGroup sg = new SpaceGroup(-1, NEW_NO_HALL_GROUP, true); sg.doNormalize = false; String[] xyzlist = xyzList.split(";"); for (int i = 0, n = xyzlist.length; i < n; i++) { SymmetryOperation op = new SymmetryOperation(null, i, false); op.setMatrixFromXYZ(xyzlist[i], 0, false); sg.addOp(op, xyzlist[i], false); } return findReferenceSpaceGroup(sg.operationCount, sg.getCanonicalSeitzList(), null); } static Object getInfo(SpaceGroup sg, String spaceGroup, float[] params, boolean asMap, boolean andNonstandard) { try { if (sg != null && sg.index >= SG.length) { SpaceGroup sgReference = findReferenceSpaceGroup(sg.operationCount, sg.getCanonicalSeitzList(), sg.clegId); if (sgReference != null) sg = sgReference; } if (params != null) { if (sg == null) { if (spaceGroup.indexOf("[") >= 0) spaceGroup = spaceGroup.substring(0, spaceGroup.indexOf("[")).trim(); if (spaceGroup.equals("unspecified!")) return "no space group identified in file"; sg = determineSpaceGroupNA(spaceGroup, params); } } else if (spaceGroup.equalsIgnoreCase("ALL")) { return dumpAll(asMap); } else if (spaceGroup.equalsIgnoreCase("MAP")) { return dumpAll(true); } else if (spaceGroup.equalsIgnoreCase("ALLSEITZ")) { return dumpAllSeitz(); } else { sg = determineSpaceGroupN(spaceGroup); } if (sg == null) { SpaceGroup sgFound = createSpaceGroupN(spaceGroup, true); if (sgFound != null) sgFound = findReferenceSpaceGroup(sgFound.operationCount, sgFound.getCanonicalSeitzList(), sgFound.clegId); if (sgFound != null) sg = sgFound; } if (sg != null) { if (asMap) { return sg.dumpInfoObj(); } SB sb = new SB(); while (sg != null) { // I don't know why there would be multiples here sb.append(sg.dumpInfo()); if (sg.index >= SG.length || !andNonstandard) break; sg = determineSpaceGroupNS(spaceGroup, sg); } return sb.toString(); } return asMap ? null : "?"; } catch (Exception e) { return "?"; } } /** * * @return detailed information */ public String dumpInfo() { SB sb = new SB(); if (groupType != TYPE_SPACE) { sb.append("\ngroupType: ").append(getSpecialGroupName(groupType)); } sb.append("\nHermann-Mauguin symbol: "); if (hmSymbol == null || hmSymbolExt == null) sb.append("?"); else sb.append(hmSymbol) .append(hmSymbolExt.length() > 0 ? ":" + hmSymbolExt : ""); if (itaNumber != null) { sb.append("\ninternational table number: ").append(itaNumber) .append(itaTransform != null ? ":" + itaTransform : "") .append("\ncrystal class: " + crystalClass); } if (jmolId != null) { sb.append("\nJmol_ID: ").append(jmolId).append(" ("+itaIndex+")"); } if (clegId != null) sb.append("\nCLEG: " + clegId); sb.append("\n\n") .append(hallInfo == null ? "Hall symbol unknown" : Logger.debugging ? hallInfo.dumpInfo() : ""); sb.append("\n\n").appendI(operationCount).append(" operators") .append(hallInfo != null && !hallInfo.getHallSymbol().equals(SG_NONE) ? " from Hall symbol " + hallInfo.getHallSymbol() + " #" + jmolId : "") .append(": "); for (int i = 0; i < operationCount; i++) { sb.append("\n").append(matrixOperations[i].xyz); } //sb.append("\n\ncanonical Seitz: ").append((String) info) //sb.append("\n----------------------------------------------------\n"); return sb.toString(); } /** * * @return detailed information */ Object dumpInfoObj() { Object info = dumpCanonicalSeitzList(); if (info instanceof SpaceGroup) return ((SpaceGroup) info).dumpInfoObj(); Map map = new Hashtable(); if (itaNumber != null && !itaNumber.equals("0")) { String s = (hmSymbol == null || hmSymbolExt == null ? "?" : hmSymbol + (hmSymbolExt.length() > 0 ? ":" + hmSymbolExt : "")); map.put("index", Integer.valueOf(index)); map.put("hm", s); map.put(JC.INFO_HM, s); map.put(JC.INFO_ITA, Integer.valueOf(PT.parseInt(itaNumber))); if (hallInfo != null && hallInfo.getHallSymbol() != null) map.put(JC.INFO_HALL, hallInfo.getHallSymbol()); if (hallSymbolAlt != null) map.put("HallSymbolAlt", hallSymbolAlt); map.put("itaIndex", itaIndex == null ? "n/a" : itaIndex); map.put("clegId", itaIndex == null ? "n/a" : clegId); if (jmolId != null) map.put("jmolId", jmolId); if (crystalClass != null) map.put("crystalClass", crystalClass); map.put("operationCount", Integer.valueOf(operationCount)); } Lst lst = new Lst(); for (int i = 0; i < operationCount; i++) { lst.addLast(matrixOperations[i].xyz); } map.put("operationsXYZ", lst); return map; } /** * CIF writer only. * * @param type * @param uc * @return HM, ITA number, or Hall symbol */ String getCIFWriterValue(String type, SymmetryInterface uc) { String ret = null; switch (type) { case JC.INFO_HM: ret = hmSymbol; break; case JC.INFO_ITA: ret = itaNumber; break; case JC.INFO_HALL: ret = hallSymbol; break; } if (ret != null) return ret; // find the space group using canonical Seitz if (info == null) { info = getInfo(this, hmSymbol, uc.getUnitCellParams(), true, false); } if (info instanceof String) return null; @SuppressWarnings("unchecked") Map map = (Map) info; Object v = map.get(type); return (v == null ? null : v.toString()); } // private String getCode() { // Map map = new Hashtable(); // for (int i = 0; i < operationCount; i++) { // String code = operations[i].getCode(); // int[] c = map.get(code); // if (c == null) { // map.put(code, c = new int[] {0}); // } // c[0]++; // } // Set keys = map.keySet(); // String[] a = keys.toArray(new String[keys.size()]); // Arrays.sort(a); // String s = ""; // for (int i = 0; i < a.length; i++) { // s += a[i] + ":" + map.get(a[i])[0] + ";"; // } // return s; // } String getName() { return name; } /* int getLatticeParameter() { return latticeParameter; } char getLatticeCode() { return latticeCode; } */ String getShelxLATTDesignation() { return HallInfo.getLatticeDesignation(latticeParameter); } void setLatticeParam(int latticeParameter) { // this does not work, because it clears the operations. // Wien2K and Shelx readers only // implication here is that we do NOT have a Hall symbol. // so we generate one. // The idea here is that we can represent any LATT number // as a simple set of rotation/translation operations this.latticeParameter = latticeParameter; if (latticeParameter > 10) // use negative this.latticeParameter = -HallInfo.getLatticeIndexFromCode(latticeParameter); } ///// private methods ///// /** * * @return either a String or a SpaceGroup, depending on index. */ private String dumpCanonicalSeitzList() { if (nHallOperators != null && hallSymbol != null) { hallInfo = new HallInfo(hallSymbol); generateAllOperators(null); } String s = getCanonicalSeitzList(); if (index >= SG.length) { SpaceGroup sgReference = findReferenceSpaceGroup(operationCount, s, clegId); if (sgReference != null) return sgReference.getCanonicalSeitzList(); } return (index >= 0 && index < SG.length ? hallSymbol + " = " : "") + s; } /** * Technically, some of these are non-reference settings, but in terms of * Jmol, they are references - the ones loaded statically. * * @return a known space group or null */ SpaceGroup getReferenceSpaceGroup() { if (referenceIndex == SG_ITA || index >= 0 && index < SG.length || modDim > 0 || matrixOperations == null || matrixOperations.length == 0 || matrixOperations[0].timeReversal != 0) return this; if (finalOperations != null) setFinalOperations(); String s = getCanonicalSeitzList(); return (s == null ? null : findReferenceSpaceGroup(operationCount, s, clegId)); } private String getCanonicalSeitzList() { return getCanonicalSeitzForOperations(matrixOperations, operationCount); } static String getCanonicalSeitzForOperations(SymmetryOperation[] operations, int n) { String[] list = new String[n]; for (int i = 0; i < n; i++) list[i] = SymmetryOperation.dumpSeitz(operations[i], true); Arrays.sort(list, 0, n); SB sb = new SB().append("\n["); for (int i = 0; i < n; i++) sb.append(list[i].replace('\t',' ').replace('\n',' ')).append("; "); sb.append("]"); return sb.toString(); } /** * * @param opCount * @param s * @param clegId * may be null if this is setting-independent * @return the matching space group if found, or null */ private synchronized static SpaceGroup findReferenceSpaceGroup(int opCount, String s, String clegId) { //getSpaceGroups(); Lst lst = htByOpCount.get(Integer.valueOf(opCount)); if (lst != null) for (int i = 0, n = lst.size(); i < n; i++) { SpaceGroup sg = lst.get(i); if (clegId != null && clegId.equals(sg)) return SG[sg.index]; if (sg.clegId == null || clegId == null || clegId.equals("0:a,b,c")) { String sgi = getCanonicalSeitz(sg.index); if (sgi.indexOf(s) >= 0) { return SG[sg.index]; } } } return null; } private final static Object dumpAll(boolean asMap) { //getSpaceGroups(); if (asMap) { Lst info = new Lst(); for (int i = 0; i < SG.length; i++) info.addLast(SG[i].dumpInfoObj()); return info; } SB sb = new SB(); for (int i = 0; i < SG.length; i++) sb.append("\n----------------------\n" + SG[i].dumpInfo()); return sb.toString(); } private final static String dumpAllSeitz() { //getSpaceGroups(); SB sb = new SB(); for (int i = 0; i < SG.length; i++) sb.append("\n").appendO(getCanonicalSeitz(i)); return sb.toString(); } private static String[] canonicalSeitzList; private static String getCanonicalSeitz(int i) { if (canonicalSeitzList == null) canonicalSeitzList = new String[SG.length]; String cs = canonicalSeitzList[i]; return (cs == null ? canonicalSeitzList[i] = SG[i].dumpCanonicalSeitzList() .toString() : cs); } private void setLattice(char latticeCode, boolean isCentrosymmetric) { //this.latticeCode = latticeCode; latticeParameter = HallInfo.getLatticeIndex(latticeCode); if (!isCentrosymmetric) latticeParameter = -latticeParameter; } final static SpaceGroup createSpaceGroupN(String name, boolean allowHall) { //getSpaceGroups(); name = name.trim(); SpaceGroup sg = determineSpaceGroupN(name); if (sg == null && allowHall) { // try unconventional Hall symbol HallInfo hallInfo = newHallInfo(name); if (hallInfo.isGenerated()) { sg = new SpaceGroup(-1, NEW_HALL_GROUP + name, true); sg.hallInfo = hallInfo; sg.hallSymbol = hallInfo.getHallSymbol(); sg.setName("[" + sg.hallSymbol + "]"); sg.jmolId = null; } else if (name.indexOf(",") >= 0) { sg = new SpaceGroup(-1, NEW_NO_HALL_GROUP, true); sg.doNormalize = false; sg.generateOperatorsFromXyzInfo(name); } } if (sg != null) { try { sg.generateAllOperators(null); return sg; } catch (Exception e) { } } return null; } protected int addOperation(String xyz0, int opId, boolean allowScaling) { if (xyz0 == null || xyz0.length() < 3) { init(false); return -1; } xyz0 = PT.rep(xyz0, " ", ""); boolean isSpecial = (xyz0.charAt(0) == '='); if (isSpecial) xyz0 = xyz0.substring(1); int id = checkXYZlist(xyz0); if (id >= 0) return id; if (xyz0.startsWith("x1,x2,x3,x4") && modDim == 0) { xyzList.clear(); operationCount = 0; modDim = PT.parseInt(xyz0.substring(xyz0.lastIndexOf("x") + 1)) - 3; } else if (xyz0.indexOf("m") >= 0) { // accept ",+m" or ",m" or ",-m" xyz0 = PT.rep(xyz0, "+m", "m"); if (xyz0.equals("x,y,z,m") || xyz0.equals("x,y,z(mx,my,mz)")) { xyzList.clear(); operationCount = 0; } } SymmetryOperation op = new SymmetryOperation(null, opId, doNormalize); if (!op.setMatrixFromXYZ(xyz0, modDim, allowScaling)) { Logger.error("couldn't interpret symmetry operation: " + xyz0); return -1; } if (xyz0.charAt(0) == '!') { xyz0 = xyz0.substring(xyz0.lastIndexOf('!') + 1); } return addOp(op, xyz0, isSpecial); } private int checkXYZlist(String xyz) { // problem was that in the case we are adding two half-cell translations, // we will get 2/2 --> nothing, instead of 1. return (xyzList.containsKey(xyz)// && !(latticeOp > 0 && xyz.indexOf("/") < 0) ? xyzList.get(xyz).intValue() : -1); } private int addOp(SymmetryOperation op, String xyz0, boolean isSpecial) { String xyz = op.xyz; if (!isSpecial) { // ! in character 0 indicates we are using the symop() function and want to be explicit int id = checkXYZlist(xyz); if (id >= 0) return id; if (latticeOp < 0) { // do this check until we find a lattice operation // by removing +1/2 and +1/3 and checking for something we already have. String xxx = PT.replaceAllCharacters( modDim > 0 ? SymmetryOperation.replaceXn(xyz, modDim + 3) : xyz, "+123/", ""); if (xyzList.containsKey(xxx + "!")) { latticeOp = operationCount; } else { xyzList.put(xxx + "!", Integer.valueOf(operationCount)); } } xyzList.put(xyz, Integer.valueOf(operationCount)); } if (!xyz.equals(xyz0)) xyzList.put(xyz0, Integer.valueOf(operationCount)); if (matrixOperations == null) matrixOperations = new SymmetryOperation[4]; if (operationCount == matrixOperations.length) matrixOperations = (SymmetryOperation[]) AU.arrayCopyObject(matrixOperations, operationCount * 2); matrixOperations[operationCount++] = op; op.number = operationCount; // check for initialization of group without time reversal if (op.timeReversal != 0) matrixOperations[0].timeReversal = 1; if (Logger.debugging) Logger.debug("\naddOperation " + operationCount + op.dumpInfo()); return operationCount - 1; } private void generateOperatorsFromXyzInfo(String xyzInfo) { init(true); String[] terms = PT.split(xyzInfo.toLowerCase(), ";"); for (int i = 0; i < terms.length; i++) addSymmetry(terms[i], 0, false); } /// operation based on Hall name and unit cell parameters only private void generateAllOperators(HallInfo h) { if (h == null) { if (operationCount > 0) return; if (hallSymbol == null || hallSymbol.endsWith("?")) { checkHallOperators(); return; } matrixOperations = new SymmetryOperation[4]; if (hallInfo == null || !hallInfo.isGenerated()) hallInfo = newHallInfo(hallSymbol); setLattice(hallInfo.getLatticeCode(), hallInfo.isCentrosymmetric()); init(true); h = hallInfo; } h.generateAllOperators(this); if (hmSymbol == null) { hmSymbol = SG_NONE; } if (hmSymbol.equals(SG_NONE)) { hallSymbol = h.getHallSymbol(); nHallOperators = Integer.valueOf(operationCount); } if (nHallOperators != null && operationCount != nHallOperators.intValue()) Logger.error("Operator mismatch " + operationCount + " for " + this); char code = h.getLatticeCode(); switch (code) { case '\0': case 'S': case 'T': case 'P': latticeType = 'P'; break; default: latticeType = code; break; } } int addSymmetrySM(String xyz, M4 operation) { int iop = addOperation(xyz, 0, false); if (iop >= 0) { SymmetryOperation symmetryOperation = matrixOperations[iop]; symmetryOperation.setM4(operation); } return iop; } final static SpaceGroup determineSpaceGroupN(String name) { return determineSpaceGroup(name, 0, 0, 0, 0, 0, 0, -1); } private final static SpaceGroup determineSpaceGroupNS(String name, SpaceGroup sg) { return determineSpaceGroup(name, 0, 0, 0, 0, 0, 0, sg.index); } final static SpaceGroup determineSpaceGroupNA(String name, float[] unitCellParams) { return (unitCellParams == null ? determineSpaceGroup(name, 0, 0, 0, 0, 0, 0, -1) : determineSpaceGroup(name, unitCellParams[0], unitCellParams[1], unitCellParams[2], unitCellParams[3], unitCellParams[4], unitCellParams[5], -1)); } private final static SpaceGroup determineSpaceGroup(String name, float a, float b, float c, float alpha, float beta, float gamma, int lastIndex) { int i = determineSpaceGroupIndex(name, a, b, c, alpha, beta, gamma, lastIndex); return (i >= 0 ? SG[i] : null); } private final static int NAME_UNK = 0; private final static int NAME_HM = 3; private final static int NAME_ITA = 4; private final static int NAME_HALL = 5; private final static int NAME_CLEG = 6; static boolean isXYZList(String name) { return (name != null && name.indexOf(",") >= 0 && name.indexOf("(") < 0 && name.indexOf(":") < 0); } private final static int determineSpaceGroupIndex(String name, float a, float b, float c, float alpha, float beta, float gamma, int lastIndex) { if (isXYZList(name)) return -1; //getSpaceGroups(); if (lastIndex < 0) lastIndex = SG.length; if (getExplicitSpecialGroupType(name) > TYPE_SPACE) return -1; name = name.trim().toLowerCase(); //boolean checkBilbao = false; if (name.startsWith("bilbao:")) { // checkBilbao = true; name = name.substring(7); } int i; int pt = name.indexOf("hall:"); if (pt > 0) name = name.substring(pt); int nameType = (name.indexOf(",") >= 0 ? NAME_CLEG : name.startsWith("ita/") ? NAME_ITA : name.startsWith("hall:") ? NAME_HALL : name.startsWith("hm:") ? NAME_HM : NAME_UNK); switch (nameType) { case NAME_CLEG: name = canonicalizeCleg(name); break; case NAME_HM: case NAME_HALL: case NAME_ITA: name = name.substring(nameType); break; case NAME_UNK: if (name.contains("[")) { // feeding back "P 1 [P 1]" for example nameType = NAME_HALL; name = name.substring(0, name.indexOf("[")).trim(); } else if (name.indexOf(".") > 0) { // 151.1 or 152.1:a,b,c;0,0,-1/6 nameType = NAME_ITA; } } switch (nameType) { case NAME_CLEG: for (i = 0; i < lastIndex; i++) { if (name.equals(SG[i].canonicalCLEG)) return i; } return -1; case NAME_HALL: for (i = 0; i < lastIndex; i++) { if (SG[i].hallSymbol.equalsIgnoreCase(name)) return i; } return -1; } String nameExt = name; boolean haveExtension = false; if (nameType == NAME_ITA) { } else { // '_' --> ' ' name = name.replace('_', ' '); // get lattice term to upper case and separated if (name.length() >= 2) { i = (name.indexOf("-") == 0 ? 2 : 1); if (i < name.length() && name.charAt(i) != ' ') name = name.substring(0, i) + " " + name.substring(i); name = toCap(name, 2); } } // get :x extension String ext = ""; if ((i = name.indexOf(":")) > 0) { ext = name.substring(i + 1); name = name.substring(0, i).trim(); haveExtension = (ext.length() > 0); } if (nameType != NAME_ITA && nameType != NAME_HALL && !haveExtension && PT.isOneOf(name, ambiguousHMNames)) { ext = "?"; haveExtension = true; } // generate spaceless abbreviation "P m m m" --> "Pmmm" "P 2(1)/c" --> "P21/c" String abbr = PT.replaceAllCharacters(name, " ()", ""); SpaceGroup s; // exact matches: switch (nameType) { case NAME_ITA: if (haveExtension) for (i = 0; i < lastIndex; i++) { if (nameExt.equalsIgnoreCase(SG[i].itaIndex)) return i; } else for (i = 0; i < lastIndex; i++) { if (name.equalsIgnoreCase(SG[i].itaIndex)) return i; } break; case NAME_CLEG: case NAME_HALL: // done already break; default: case NAME_HM: // Full intl table entry, including :xx if (nameType != NAME_HM) for (i = 0; i < lastIndex; i++) if (SG[i].jmolId.equalsIgnoreCase(nameExt)) return i; // Full H-M symbol, including :xx // BUT some on the list presume defaults. The way to finesse this is // to add ":?" to a space group name to force axis ambiguity check for (i = 0; i < lastIndex; i++) if (SG[i].hmSymbolFull.equalsIgnoreCase(nameExt)) return i; // alternative, but unique H-M symbol, specifically for F m 3 m/F m -3 m type for (i = 0; i < lastIndex; i++) if ((s = SG[i]).hmSymbolAlternative != null && s.hmSymbolAlternative.equalsIgnoreCase(nameExt)) return i; if (haveExtension) { // P2/m:a // Abbreviated H-M with intl table :xx for (i = 0; i < lastIndex; i++) if ((s = SG[i]).hmSymbolAbbr.equalsIgnoreCase(abbr) && (s.hmSymbolExt.equalsIgnoreCase(ext) || s.jmolIdExt.equalsIgnoreCase(ext))) return i; // shortened -- not including " 1 " terms for (i = 0; i < lastIndex; i++) if ((s = SG[i]).hmSymbolAbbrShort.equalsIgnoreCase(abbr) && (s.hmSymbolExt.equalsIgnoreCase(ext) || s.jmolIdExt.equalsIgnoreCase(ext))) return i; } // unique axis, cell and origin options with H-M abbr char uniqueAxis = determineUniqueAxis(a, b, c, alpha, beta, gamma); if (!haveExtension || ext.charAt(0) == '?') // no extension or unknown extension, so we look for unique axis for (i = 0; i < lastIndex; i++) if (((s = SG[i]).hmSymbolAbbr.equalsIgnoreCase(abbr) || s.hmSymbolAbbrShort.equalsIgnoreCase(abbr) || s.itaNumber.equals(abbr)) //&& (!checkBilbao || s.isBilbao) ) switch (s.ambiguityType) { case '\0': case '-': return i; case 'a': if (s.uniqueAxis == uniqueAxis || uniqueAxis == '\0') return i; break; case 'o': if (ext.length() == 0) { if (s.hmSymbolExt.equals("2")) return i; // defaults to origin:2 } else if (s.hmSymbolExt.equalsIgnoreCase(ext)) return i; break; case 't': if (ext.length() == 0) { if (s.axisChoice == 'h') return i; //defaults to hexagonal } else if ((s.axisChoice + "").equalsIgnoreCase(ext)) return i; break; } break; } // inexact just the number; no extension indicated -- first in list if (ext.length() == 0) for (i = 0; i < lastIndex; i++) if ((s = SG[i]).itaNumber.equals(nameExt) //&& (!checkBilbao || s.isBilbao) ) return i; return -1; } private void setJmolCode(String name) { jmolId = name; String[] parts = PT.split(name, ":"); itaNumber = parts[0]; jmolIdExt = (parts.length == 1 ? "" : parts[1]); ambiguityType = '\0'; if (jmolIdExt.length() > 0) { char c = jmolIdExt.charAt(0); if (jmolIdExt.equals("h") || jmolIdExt.equals("r")) { ambiguityType = 't'; axisChoice = jmolIdExt.charAt(0); } else if (c == '1' || c == '2') { ambiguityType = 'o'; // originChoice = intlTableNumberExt.charAt(0); } else if (jmolIdExt.length() <= 2 || jmolIdExt.length() == 3 && c == '-' ) { // :a or :b3 ambiguityType = 'a'; uniqueAxis = jmolIdExt.charAt(c == '-' ? 1 : 0); // Q: should we include :-a1 here? // if (intlTableNumberExt.length() == 2) // cellChoice = intlTableNumberExt.charAt(1); } else if (jmolIdExt.contains("-")) { ambiguityType = '-'; // skip when searching for a group by name // added 9/28/14 Jmol 14.3.7 } } } private final static char determineUniqueAxis(float a, float b, float c, float alpha, float beta, float gamma) { if (a == b) return (b == c ? '\0' : 'c'); if (b == c) return 'a'; if (c == a) return 'b'; if (alpha == beta) return (beta == gamma ? '\0' : 'c'); if (beta == gamma) return 'a'; if (gamma == alpha) return 'b'; return '\0'; } /// data /// private volatile static int sgIndex = -1; private volatile static String lastInfo; private final static String SET_AB = "a-b,a+b,c"; /** * For example P 1 2 1 and P 2, meaning P 2 is somewhat ambiguous (without knowning the standard) */ private volatile static String ambiguousHMNames = ""; private volatile static String lastHallSymbol = ""; private void buildSelf(String sgLineData) { String[] terms = PT.split(sgLineData.toLowerCase(), ";"); jmolId = terms[0].trim(); // International Table Number : // options // "0 ;-- ;-- ;0 ;-- ;-- ;" // intlNo:options;itaIndex;transform;nOps;schoenflies;hermannMauguin;Hall // 0 1 2 3 4 5 // added # of operators to help in search phase // "4:b;4.1;2;c2^2;p 1 21 1;p 2yb", //full name //// terms[0] -- International Table Number and setting //// setJmolCode(jmolId); boolean isAlternate = jmolId.endsWith("*"); if (isAlternate) jmolId = jmolId.substring(0, jmolId.length() - 1); //// terms[1] -- ITA index or '--' //// // could be "154:a,b,c|0,0,-1/6" itaIndex = terms[1].replace('|',';'); //// terms[2] -- transform String s = terms[2]; // leaving "r" as is itaTransform = (s.length() == 0 || s.equals(SG_NONE) ? "a,b,c" : s.equals("r") ? SimpleUnitCell.HEX_TO_RHOMB : PT.rep(s, "ab", SET_AB).replace('|', ';')); setClegId(itaNumber + ":" + itaTransform); //// terms[3] -- number of operators //// if (terms[3].length() > 0) { nHallOperators = Integer.valueOf(terms[3]); Lst lst = htByOpCount.get(nHallOperators); if (lst == null) htByOpCount.put(nHallOperators, lst = new Lst()); lst.addLast(this); } //// terms[4] -- Schoenflies //// crystalClass = toCap(PT.split(terms[4], "^")[0], 1); //// terms[5] -- Hermann-Mauguin //// String hm = terms[5]; if (hm.endsWith("*")) hm = hm.substring(0, hm.length() - 1); setHMSymbol(hm); //// term 6 -- Hall //// String info; if ("xyz".equals(terms[6])) { info = hmSymbol; hallSymbol = "" + latticeType + "?"; // hallInfo will be used to apply lattice } else { hallSymbol = terms[6]; if (hallSymbol.length() > 1) hallSymbol = toCap(hallSymbol, 2); if (isAlternate) { hallSymbolAlt = hallSymbol; hallSymbol = lastHallSymbol; } info = itaNumber + hallSymbol; if (itaNumber.charAt(0) != '0' && info.equals(lastInfo)) { isAlternate = true; ambiguousHMNames += hmSymbol + ";"; } } lastHallSymbol = hallSymbol; // terms[6] operator list where I ddn't figure out the Hall code lastInfo = info; name = "HM:" + hmSymbolFull + " " + (hallSymbol == null || hallSymbol == "?" ? "[" + hallSymbol + "]" : "") + " #" + itaIndex; } void setHMSymbol(String name) { int pt = name.indexOf("#"); if (pt >= 0) name = name.substring(0, pt).trim(); hmSymbolFull = (groupType == TYPE_SPACE ? toCap(name, 1) : name.toLowerCase()); latticeType = Character.toUpperCase(hmSymbolFull.charAt(0)); String[] parts = PT.split(hmSymbolFull, ":"); hmSymbol = parts[0]; hmSymbolExt = (parts.length == 1 ? "" : parts[1]); pt = hmSymbol.indexOf(" -3"); if (pt >= 1) if ("admn".indexOf(hmSymbol.charAt(pt - 1)) >= 0) { hmSymbolAlternative = (hmSymbol.substring(0, pt) + " 3" + hmSymbol .substring(pt + 3)).toLowerCase(); } hmSymbolAbbr = PT.rep(hmSymbol, " ", ""); hmSymbolAbbrShort = (hmSymbol.length() > 3 ? PT.rep(hmSymbol, " 1", "") : hmSymbolAbbr); hmSymbolAbbrShort = PT.rep(hmSymbolAbbrShort, " ", ""); strName = null; } private static String toCap(String s, int n) { return s.substring(0, n).toUpperCase() + s.substring(n); } @Override public String toString() { return asString(); } String strName; public String displayName; public static final String PREFIX_FRIEZE = "f/"; public static final String PREFIX_ROD = "r/"; public static final String PREFIX_LAYER = "l/"; public static final String PREFIX_PLANE = "p/"; public static final String PREFIX_SPACE = ""; public static final int TYPE_FRIEZE = 600; public static final int TYPE_ROD = 500; public static final int TYPE_LAYER = 400; public static final int TYPE_PLANE = 300; public static final int TYPE_SPACE = 0; public static final int TYPE_INVALID = -1; public String asString() { return (strName == null ? (strName = (jmolId == null || jmolId.equals("0") ? name : jmolId + " HM:" + hmSymbolFull + (getClegId() == null ? "" : " #" + getClegId()) ) ) : strName ); } public String getDisplayName() { if (displayName == null) { String name = null; if (jmolId == null || SG_NONE.equals(hallSymbol)) { name = ""; if (hmSymbolFull != null && !SG_NONE.equals(hmSymbol)) name = hmSymbolFull; } else if (!jmolId.equals("0")) { name = //jmolId + " HM: " + hmSymbolFull; } if (name == null) { name = "[" + hallSymbol + "]"; // may still need setting } else if (getClegId() != null){ name += " #" + getClegId(); } if (name.endsWith(SimpleUnitCell.HEX_TO_RHOMB)) name = PT.rep(name, SimpleUnitCell.HEX_TO_RHOMB, "r"); if (name.indexOf(NO_NAME) >= 0) name = ""; if (name.endsWith(":a,b,c")) name = name.substring(0, name.length() - 6); displayName = name; } return displayName; } private static SpaceGroup[] SG; private static Map> htByOpCount = new Hashtable>(); static Map nameToGroup; static int nSG = 0; private synchronized static SpaceGroup[] getSpaceGroups() { if (SG == null) { int n = STR_SG.length; nameToGroup = new Hashtable(); SpaceGroup[] defs = new SpaceGroup[n]; for (int i = 0; i < n; i++) { defs[i] = new SpaceGroup(i, STR_SG[i], true); nameToGroup.put(defs[i].jmolId, defs[i]); } System.out.println("SpaceGroup - " + n + " settings generated"); STR_SG = null; SG = defs; } return SG; } /** * * @param lattvecs * could be magnetic centering, in which case there is an additional * lattice parameter that is time reversal * @return true if successful */ public boolean addLatticeVectors(Lst lattvecs) { if (latticeOp >= 0 || lattvecs.size() == 0) return false; int nOps = latticeOp = operationCount; boolean isMagnetic = (lattvecs.get(0).length == modDim + 4); int magRev = -2; for (int j = 0; j < lattvecs.size(); j++) { float[] data = lattvecs.get(j); if (isMagnetic) { magRev = (int) data[modDim + 3]; data = AU.arrayCopyF(data, modDim + 3); } if (data.length > modDim + 3) return false; for (int i = 0; i < nOps; i++) { SymmetryOperation newOp = new SymmetryOperation(null, 0, true); // must normalize these newOp.modDim = modDim; SymmetryOperation op = matrixOperations[i]; newOp.divisor = op.divisor; newOp.linearRotTrans = AU.arrayCopyF(op.linearRotTrans, -1); newOp.setFromMatrix(data, false); if (magRev != -2) newOp.setTimeReversal(op.timeReversal * magRev); newOp.xyzOriginal = newOp.xyz; addOp(newOp, newOp.xyz, true); } } return true; } int getSiteMultiplicity(P3 pt, UnitCell unitCell) { int n = finalOperations.length; Lst pts = new Lst(); for (int i = n; --i >= 0;) { P3 pt1 = P3.newP(pt); finalOperations[i].rotTrans(pt1); unitCell.unitize(pt1); for (int j = pts.size(); --j >= 0;) { P3 pt0 = pts.get(j); if (pt1.distanceSquared(pt0) < JC.UC_TOLERANCE2) {// was 0.000001f) { pt1 = null; break; } } if (pt1 != null) pts.addLast(pt1); } return n / pts.size(); } void setName(String name) { this.name = name; if (name != null && name.startsWith("HM:")) { setHMSymbol(name.substring(3)); } strName = displayName = null; } /** * Look for Jmol ID such as 10:b or 10 or 10.2 or 10:c,a,b * @param vwr * @param name * * @return found space group or null */ static SpaceGroup getSpaceGroupFromJmolClegOrITA(Viewer vwr, String name) { int specialType = getExplicitSpecialGroupType(name); String s = (specialType > TYPE_SPACE ? name.substring(2) : name); int ptCleg = s.indexOf(":"); int ptTrm = s.indexOf(","); int ptIndex = s.indexOf("."); int pt = (ptCleg > 0 && ptTrm > ptCleg ? ptCleg : ptIndex); int itno = getITNo(s, pt); int itindex = (pt > 0 && pt == ptCleg || itno == Integer.MIN_VALUE ? 0 : pt > 0 ? getITNo(s.substring(pt + 1), 0) : 1); if (specialType > TYPE_SPACE) { return Symmetry.getSGFactory().getSpecialGroup(null, vwr, name, itno, itindex, pt > 0 && pt == ptCleg, specialType); } int n = SG.length; if (pt > 0 && pt == ptCleg) { // 10:c,a,b for (int i = 0; i < n; i++) { if (name.equals(SG[i].clegId)) return SG[i]; } } else if (ptCleg > 0) { // 10:b for (int i = 0; i < n; i++) { if (name.equals(SG[i].jmolId)) return SG[i]; } } else if (ptIndex > 0) { // 10.3 for (int i = 0; i < n; i++) if (name.equals(SG[i].itaIndex)) return SG[i]; } else { // just first match to ita number for (int i = 0; i < n; i++) if (name.equals(SG[i].itaNumber)) return SG[i]; } return null; } void checkHallOperators() { if (nHallOperators != null && nHallOperators.intValue() != operationCount) { if (hallInfo == null || hallInfo.isGenerated()) { generateAllOperators(hallInfo); } else { // using ITA data, not Hall operators init(false); doNormalize = true; // get base ITA nnn.1 + transform, setting my operators // I have all my information already. transformSpaceGroup(TYPE_SPACE, this, getSpaceGroupFromJmolClegOrITA(null, itaNumber), null, itaTransform, null); hallInfo = null; } } } /** * This method is used to generate the additional operators needed to cover * subgroups and some settings with dimension other than 1. * * It back-transforms the subgroup to the group and then returns it to the * subgroup, adding all the necessary operations. * * It is used specifically by ModelKit.cmdAssignSpaceGroupPacked for packing * the unit cell of a space group. * * @param transform * @return full set of operators for this transformation. */ M4[] getOpsCtr(String transform) { SpaceGroup sg = getNull(true, true, false); transformSpaceGroup(groupType, sg, this, null, "!" + transform, null); sg.setFinalOperations(); SpaceGroup sg2 = getNull(true, false, false); transformSpaceGroup(groupType, sg2, sg, null, transform, null); sg2.setFinalOperations(); return sg2.finalOperations; } static SpaceGroup getSpaceGroupFromIndex(int i) { return (SG != null && i >= 0 && i < SG.length ? SG[i] : null); } /** * NOTE: SpecialPrefix must be set before this method is executed. * * from SpaceGroupFinder after finding a match with an ITA setting * @param jmolId * @param sg * @param set * @param tr */ void setITATableNames(String jmolId, String sg, String set, String tr) { itaNumber = sg; itaIndex = (tr != null ? sg + ":" + tr : set.indexOf(".") >= 0 ? set : sg + "." + set); itaTransform = tr; setClegId(specialPrefix + sg + ":" + tr); strName = displayName = null; this.jmolId = jmolId; if (jmolId == null) { name = clegId; info = dumpInfoObj(); } else { setJmolCode(jmolId); } } static Lst transformCoords(Lst coord, M4 trmInv, P3 centering, M4 t, float[] v, Lst coordt) { if (coordt == null) coordt = new Lst<>(); for (int j = 0, n = coord.size(); j < n; j++) { String xyz = SymmetryOperation.transformStr((String) coord.get(j), null, trmInv, t, v, null, centering, true, true); if (!coordt.contains(xyz)) coordt.addLast(xyz); } return coordt; } /** * We sum the M3 column vectors. The result is (a' + b' + * c'), which is the diagonal vector across the unit cell in the coordinates * of the original lattice. Values are obtained for negative and pasitive ranges * * * This method is used for two purpose: * * 1) When a subgroup transformation or setting is made that enlarges the unit * cell, this method delivers the additional centering information that may be * needed to generate additional operators. * * 2) When a transformed space group unit cell is packed, this result gives us * the information we need to pack that cell fully, drawing from atoms that * are in all the covered original unit cells. * * For example, P42(77) has a 45-degree rotated setting C42. * * https://www.cryst.ehu.es/cgi-bin/cryst/programs//nph-trgen?gnum=077&what=gp&trmat=a-b,a+b,c&unconv=C%2042&from=ita * * The transformation matrix is a-b,a+b,c;0,0,0. Summing this, we get * [0,-1,0](neg) and [2,1,1](pos). The range of cells needed to cover this is [0,1,2), [-1,1), [0,1) * * @param trm * @return the range as float[][], or null if the result would be [0 0 0][1 1 1] */ static float[][] getTransformRange(M4 trm) { float[][] t = new float[2][3]; float[] row = new float[4]; for (int i = 0; i < 3; i++) { trm.getRow(i, row); for (int j = 0; j < 3; j++) { float v = row[j]; if (v < 0) { t[0][i] += -row[j]; } else if (v > 0) { t[1][i] += row[j]; } } } boolean ignore = true; for (int i = 0, dz = 0; i < 2; i++, dz++) { for (int j = 0; j < 3; j++) { int d = (int) Math.ceil(t[i][j]); if (d > dz) ignore = false; t[i][j] = (i == 0 ? -d : d); } } return (ignore ? null : t); } /** * adjust centering based on transformation * * @param trm * @param cent list to be revised * @return trmInv */ private static M4 getTransformedCentering(M4 trm, Lst cent) { M4 trmInv = M4.newM4(trm); trmInv.invert(); int n0 = cent.size(); P3 pc = new P3(); P3 p = new P3(); float[][] c = getTransformRange(trm); if (c != null) { int n = addCentering(trmInv, c, pc, p, cent, 0); for (int i = n0; --i >= 0 && n < 3;) { SymmetryOperation.toPoint((String) cent.remove(i), pc); n = addCentering(trmInv, c, pc, p, cent, n); } } return trmInv; } private static int addCentering(M4 trmInv, float[][] c, P3 pc, P3 p, Lst cent, int n) { for (int i = (int) c[0][0]; i <= c[1][0]; i++) { for (int j = (int) c[0][1]; j <= c[1][1]; j++) { for (int k = (int) c[0][2]; k <= c[1][2]; k++) { p.set(i, j, k); p.add(pc); trmInv.rotTrans(p); if (p.length() % 1 != 0) { p.x = p.x % 1; p.y = p.y % 1; p.z = p.z % 1; String s = SymmetryOperation.norm3(p); if (!s.equals("0,0,0") && !cent.contains(s)) { cent.addLast(s); if (++n == 3) return 3; } } } } } return n; } /** * Create a Wyckoff information map for a setting that is not in the ITA (at * least not in the General Position list.) * * Check is that 100:a+b,a-b,c comes out right. * * The task is three-fold: * * 1) find the centering * * 2) apply the operations * * 3) update the multiplicities * @param vwr * @param map to fill or null * @param clegId * @param itno * @param its0 * @return new map containing just gp and wpos */ @SuppressWarnings("unchecked") static Map fillMoreData(Viewer vwr, Map map, String clegId, int itno, Map its0) { int pt = clegId.indexOf(':'); String transform = (pt < 0 ? "a,b,c" : clegId.substring(pt + 1)); M4 trm = UnitCell.toTrm(transform, null); Lst gp0 = (Lst) its0.get("gp"); Map wpos0 = (Map) its0.get("wpos"); Lst cent0 = (Lst) wpos0.get("cent"); Lst cent = new Lst<>(); if (cent0 != null) cent.addAll(cent0); int nctr0 = cent.size(); M4 trmInv = getTransformedCentering(trm, cent); int nctr = cent.size(); Lst pos0 = (Lst) wpos0.get("pos"); Lst pos = new Lst(); M4 t = new M4(); float[] v = new float[16]; float f = (nctr + 1f) / (nctr0 + 1); for (int i = 0, n = pos0.size(); i < n; i++) { Map p0 = (Map) pos0.get(i); Map p = new Hashtable(); p.putAll(p0); Lst coord = (Lst) p0.get("coord"); if (coord != null) { coord = transformCoords(coord, trmInv, null, t, v, null); p.put("coord", coord); } int mult = ((Integer) p0.get("mult")).intValue(); p.put("mult", Integer.valueOf((int) (mult * f))); pos.addLast(p); } Lst gp = new Lst(); transformCoords(gp0, trmInv, null, t, v, gp); if (nctr > 0) { for (int i = 0; i < nctr; i++) { P3 p = new P3(); transformCoords(gp0, trmInv, SymmetryOperation.toPoint((String) cent.get(i), p), t, v, gp); } } if (map == null) { map = new Hashtable(); map.put("sg", Integer.valueOf(itno)); map.put("trm", transform); map.put("clegId", itno + ":" + transform); map.put("det", Float.valueOf(trm.determinant3())); } else { map.remove("more"); } Map wpos = new Hashtable<>(); if (nctr > 0) wpos.put("cent", cent); wpos.put("pos", pos); map.put("wpos", wpos); //wpos.put("gp", gp); gp = new Lst<>(); SpaceGroup base = getSpaceGroupFromJmolClegOrITA(vwr, clegId); SpaceGroup sg = transformSpaceGroup(TYPE_SPACE, null, base, gp0, transform, new M4()); for (int i = 0, n = sg.getOperationCount(); i < n; i++) { gp.addLast(((SymmetryOperation) sg.getOperation(i)).xyz); } map.put("gp", gp); return map; } /** * Transform a space group based on a list of general postions (operations). * * If the general positions are not known, they can be taken from a base space * group instead of a list of general positions in string xyz format. * * The assumption is that they need transformation. So if the base is already * * modelkit zap spacegroup "225:p" * * @param groupType ignored if sg and base are not both null * @param sg * @param base * @param genPos * @param transform * @param trm * @return new space group */ static SpaceGroup transformSpaceGroup(int groupType, SpaceGroup sg, SpaceGroup base, Lst genPos, String transform, M4 trm) { if (genPos == null) { // here we use the operations of the known space group // when (1) this is a space group derived from a subgroup by reverse transformation // or (2) when we are using Jmol's built-in Hall operators base.setFinalOperations(); // should be able to do this much slicker genPos = new Lst(); for (int i = 0, n = base.getOperationCount(); i < n; i++) { genPos.addLast(base.getXyz(i, false)); } } boolean normalize = (sg == null || sg.doNormalize); // if sg != null, then xyzlist is not calculated and instead sg is filled. Lst xyzList = addTransformXYZList(sg, genPos, transform, trm, normalize); if (sg == null) { return createITASpaceGroup(groupType, xyzList, base); } // a null transform indicates we have the operators already, and no transformation is needed // the base space group has all the relevant information if (transform == null) { sg.setFrom(base, true); } else { // sg is presumed to be the standard setting when there is a transform sg.setITATableNames(sg.jmolId, sg.itaNumber, "1", transform); } return sg; } /** * no transformation is done * * @param groupType * @param genpos * @param base * @return cloned space group */ static SpaceGroup createITASpaceGroup(int groupType, Lst genpos, SpaceGroup base) { SpaceGroup sg = (groupType == TYPE_SPACE ? new SpaceGroup(-1, NEW_NO_HALL_GROUP, true) : Symmetry.getSGFactory().createSpecialGroup((SpecialGroup) base, null, null, groupType)); sg.doNormalize = false; for (int i = 0, n = genpos.size(); i < n; i++) { SymmetryOperation op = new SymmetryOperation(null, i, false); String xyz = (String) genpos.get(i); op.setMatrixFromXYZ(xyz, 0, false); sg.addOp(op, xyz, false); } if (base != null) sg.setFrom(base, true); return sg; } /** * Add operators based on a setting or subgroup transformation. * In cases where the det > 1, scan a range of values that encompass * the possibilities. * * @param sg * if not null, this is the space group that is being created and to be * loaded with operations * @param genPos * @param transform * @param trm * @param normalize * @return a semicolon-separated list of operations if sg is null, or null if * it is not */ private static Lst addTransformXYZList(SpaceGroup sg, Lst genPos, String transform, M4 trm, boolean normalize) { M4 trmInv = null, t = null; float[] v = null; float[][] c = null; int nTotal = genPos.size(); if (transform != null) { if (transform.equals("r")) transform = SimpleUnitCell.HEX_TO_RHOMB; trm = UnitCell.toTrm(transform, trm); trmInv = M4.newM4(trm); trmInv.invert(); int det = Math.round(trm.determinant3()); if (det > 1) { c = getTransformRange(trm); nTotal *= det; } v = new float[16]; t = new M4(); } Lst xyzList = addTransformedOperations(sg, genPos, trm, trmInv, t, v, sg == null ? new Lst() : null, null, normalize); if (c != null) { P3 p = new P3(); // scanning through a first, then b, then c for (int k = (int) c[0][2]; k <= c[1][2]; k++) { for (int j = (int) c[0][1]; j <= c[1][1]; j++) { for (int i = (int) c[0][0]; i < c[1][0]; i++) { if (i == 0 && j == 0 && k == 0) continue; p.set(i, j, k); if (addTransformedOperations(sg, genPos, trm, trmInv, t, v, xyzList, p, normalize) != null) { if (xyzList.size() == nTotal) return xyzList; } } } } } return (sg == null ? xyzList : null); } /** * add canonical (positive unitized translation) transformed operations, * either to form a list or to fill a space group. * * @param sg * space group to fill with transformed operations * @param genPos * list of operations to be transfomed * @param trm * transform matrix * @param trmInv * inverse; may be null * @param t * temp matrix * @param v * temp vector * @param retGenPos * list to append to -- only if sg == null * @param centering * centering if needed * @param normalize * to set to a standard translation and fractions * @return semicolon-separated list -- only if sg is null */ private static Lst addTransformedOperations(SpaceGroup sg, Lst genPos, M4 trm, M4 trmInv, M4 t, float[] v, Lst retGenPos, P3 centering, boolean normalize) { if (sg != null) sg.latticeOp = 0; // ignore looking for lattice operations for (int i = 0, c = genPos.size(); i < c; i++) { String xyz = (String) genPos.get(i); if (trm != null && (i > 0 || centering != null)) { xyz = SymmetryOperation.transformStr(xyz, trm, trmInv, t, v, centering, null, normalize, false); } if (sg != null) { // space group addition will disallow duplicates already. sg.addOperation(xyz, 0, false); } else if (!retGenPos.contains(xyz)) { // there could be duplicates because we don't know a priori which direction to translate. // these are canonical, so duplicates will be found and discarded. retGenPos.addLast(xyz); } } return retGenPos; } @Override public M4 getMatrixOperation(int i) { return matrixOperations[i]; } @Override public int getMatrixOperationCount() { return operationCount; } @Override public boolean addHallOperationCheckDuplicates(M4 operation) { String xyz = SymmetryOperation.getXYZFromMatrix(operation, true, true, false); if (checkXYZlist(xyz) >= 0) return false; addSymmetrySM("!nohalf!" + xyz, operation); return true; } /** * adds :a,b,c;0,0,0 or ;0,0,0; does NOT change :h or :r * @param t * @return full CLEG */ public static String canonicalizeCleg(String t) { if (t.indexOf(":") < 0) { t += ":a,b,c;0,0,0"; } else if (t.indexOf(",") > 0 && t.indexOf(";") < 0) { t += ";0,0,0"; } return t; } /* see https://cci.lbl.gov/sginfo/itvb_2001_table_a1427_hall_symbols.html https://cci.lbl.gov/sginfo/itvb_2001_table_a1427_hall_symbols.html intl# H-M full HM-abbr HM-short Hall 1 P 1 P1 P P 1 2 P -1 P-1 P-1 -P 1 3:b P 1 2 1 P121 P2 P 2y 3:b P 2 P2 P2 P 2y 3:c P 1 1 2 P112 P2 P 2 3:a P 2 1 1 P211 P2 P 2x 4:b P 1 21 1 P1211 P21 P 2yb 4:b P 21 P21 P21 P 2yb 4:b* P 1 21 1* P1211* P21* P 2y1 4:c P 1 1 21 P1121 P21 P 2c 4:c* P 1 1 21* P1121* P21* P 21 4:a P 21 1 1 P2111 P21 P 2xa 4:a* P 21 1 1* P2111* P21* P 2x1 5:b1 C 1 2 1 C121 C2 C 2y 5:b1 C 2 C2 C2 C 2y 5:b2 A 1 2 1 A121 A2 A 2y 5:b3 I 1 2 1 I121 I2 I 2y 5:c1 A 1 1 2 A112 A2 A 2 5:c2 B 1 1 2 B112 B2 B 2 5:c3 I 1 1 2 I112 I2 I 2 5:a1 B 2 1 1 B211 B2 B 2x 5:a2 C 2 1 1 C211 C2 C 2x 5:a3 I 2 1 1 I211 I2 I 2x 6:b P 1 m 1 P1m1 Pm P -2y 6:b P m Pm Pm P -2y 6:c P 1 1 m P11m Pm P -2 6:a P m 1 1 Pm11 Pm P -2x 7:b1 P 1 c 1 P1c1 Pc P -2yc 7:b1 P c Pc Pc P -2yc 7:b2 P 1 n 1 P1n1 Pn P -2yac 7:b2 P n Pn Pn P -2yac 7:b3 P 1 a 1 P1a1 Pa P -2ya 7:b3 P a Pa Pa P -2ya 7:c1 P 1 1 a P11a Pa P -2a 7:c2 P 1 1 n P11n Pn P -2ab 7:c3 P 1 1 b P11b Pb P -2b 7:a1 P b 1 1 Pb11 Pb P -2xb 7:a2 P n 1 1 Pn11 Pn P -2xbc 7:a3 P c 1 1 Pc11 Pc P -2xc 8:b1 C 1 m 1 C1m1 Cm C -2y 8:b1 C m Cm Cm C -2y 8:b2 A 1 m 1 A1m1 Am A -2y 8:b3 I 1 m 1 I1m1 Im I -2y 8:b3 I m Im Im I -2y 8:c1 A 1 1 m A11m Am A -2 8:c2 B 1 1 m B11m Bm B -2 8:c3 I 1 1 m I11m Im I -2 8:a1 B m 1 1 Bm11 Bm B -2x 8:a2 C m 1 1 Cm11 Cm C -2x 8:a3 I m 1 1 Im11 Im I -2x 9:b1 C 1 c 1 C1c1 Cc C -2yc 9:b1 C c Cc Cc C -2yc 9:b2 A 1 n 1 A1n1 An A -2yab 9:b3 I 1 a 1 I1a1 Ia I -2ya 9:-b1 A 1 a 1 A1a1 Aa A -2ya 9:-b2 C 1 n 1 C1n1 Cn C -2yac 9:-b3 I 1 c 1 I1c1 Ic I -2yc 9:c1 A 1 1 a A11a Aa A -2a 9:c2 B 1 1 n B11n Bn B -2ab 9:c3 I 1 1 b I11b Ib I -2b 9:-c1 B 1 1 b B11b Bb B -2b 9:-c2 A 1 1 n A11n An A -2ab 9:-c3 I 1 1 a I11a Ia I -2a 9:a1 B b 1 1 Bb11 Bb B -2xb 9:a2 C n 1 1 Cn11 Cn C -2xac 9:a3 I c 1 1 Ic11 Ic I -2xc 9:-a1 C c 1 1 Cc11 Cc C -2xc 9:-a2 B n 1 1 Bn11 Bn B -2xab 9:-a3 I b 1 1 Ib11 Ib I -2xb 10:b P 1 2/m 1 P12/m1 P2/m -P 2y 10:b P 2/m P2/m P2/m -P 2y 10:c P 1 1 2/m P112/m P2/m -P 2 10:a P 2/m 1 1 P2/m11 P2/m -P 2x 11:b P 1 21/m 1 P121/m1 P21/m -P 2yb 11:b P 21/m P21/m P21/m -P 2yb 11:b* P 1 21/m 1* P121/m1* P21/m* -P 2y1 11:c P 1 1 21/m P1121/m P21/m -P 2c 11:c* P 1 1 21/m* P1121/m* P21/m* -P 21 11:a P 21/m 1 1 P21/m11 P21/m -P 2xa 11:a* P 21/m 1 1* P21/m11* P21/m* -P 2x1 12:b1 C 1 2/m 1 C12/m1 C2/m -C 2y 12:b1 C 2/m C2/m C2/m -C 2y 12:b2 A 1 2/m 1 A12/m1 A2/m -A 2y 12:b3 I 1 2/m 1 I12/m1 I2/m -I 2y 12:b3 I 2/m I2/m I2/m -I 2y 12:c1 A 1 1 2/m A112/m A2/m -A 2 12:c2 B 1 1 2/m B112/m B2/m -B 2 12:c3 I 1 1 2/m I112/m I2/m -I 2 12:a1 B 2/m 1 1 B2/m11 B2/m -B 2x 12:a2 C 2/m 1 1 C2/m11 C2/m -C 2x 12:a3 I 2/m 1 1 I2/m11 I2/m -I 2x 13:b1 P 1 2/c 1 P12/c1 P2/c -P 2yc 13:b1 P 2/c P2/c P2/c -P 2yc 13:b2 P 1 2/n 1 P12/n1 P2/n -P 2yac 13:b2 P 2/n P2/n P2/n -P 2yac 13:b3 P 1 2/a 1 P12/a1 P2/a -P 2ya 13:b3 P 2/a P2/a P2/a -P 2ya 13:c1 P 1 1 2/a P112/a P2/a -P 2a 13:c2 P 1 1 2/n P112/n P2/n -P 2ab 13:c3 P 1 1 2/b P112/b P2/b -P 2b 13:a1 P 2/b 1 1 P2/b11 P2/b -P 2xb 13:a2 P 2/n 1 1 P2/n11 P2/n -P 2xbc 13:a3 P 2/c 1 1 P2/c11 P2/c -P 2xc 14:b1 P 1 21/c 1 P121/c1 P21/c -P 2ybc 14:b1 P 21/c P21/c P21/c -P 2ybc 14:b2 P 1 21/n 1 P121/n1 P21/n -P 2yn 14:b2 P 21/n P21/n P21/n -P 2yn 14:b3 P 1 21/a 1 P121/a1 P21/a -P 2yab 14:b3 P 21/a P21/a P21/a -P 2yab 14:c1 P 1 1 21/a P1121/a P21/a -P 2ac 14:c2 P 1 1 21/n P1121/n P21/n -P 2n 14:c3 P 1 1 21/b P1121/b P21/b -P 2bc 14:a1 P 21/b 1 1 P21/b11 P21/b -P 2xab 14:a2 P 21/n 1 1 P21/n11 P21/n -P 2xn 14:a3 P 21/c 1 1 P21/c11 P21/c -P 2xac 15:b1 C 1 2/c 1 C12/c1 C2/c -C 2yc 15:b1 C 2/c C2/c C2/c -C 2yc 15:b2 A 1 2/n 1 A12/n1 A2/n -A 2yab 15:b3 I 1 2/a 1 I12/a1 I2/a -I 2ya 15:b3 I 2/a I2/a I2/a -I 2ya 15:-b1 A 1 2/a 1 A12/a1 A2/a -A 2ya 15:-b2 C 1 2/n 1 C12/n1 C2/n -C 2yac 15:-b2 C 2/n C2/n C2/n -C 2yac 15:-b3 I 1 2/c 1 I12/c1 I2/c -I 2yc 15:-b3 I 2/c I2/c I2/c -I 2yc 15:c1 A 1 1 2/a A112/a A2/a -A 2a 15:c2 B 1 1 2/n B112/n B2/n -B 2ab 15:c3 I 1 1 2/b I112/b I2/b -I 2b 15:-c1 B 1 1 2/b B112/b B2/b -B 2b 15:-c2 A 1 1 2/n A112/n A2/n -A 2ab 15:-c3 I 1 1 2/a I112/a I2/a -I 2a 15:a1 B 2/b 1 1 B2/b11 B2/b -B 2xb 15:a2 C 2/n 1 1 C2/n11 C2/n -C 2xac 15:a3 I 2/c 1 1 I2/c11 I2/c -I 2xc 15:-a1 C 2/c 1 1 C2/c11 C2/c -C 2xc 15:-a2 B 2/n 1 1 B2/n11 B2/n -B 2xab 15:-a3 I 2/b 1 1 I2/b11 I2/b -I 2xb 16 P 2 2 2 P222 P222 P 2 2 17 P 2 2 21 P2221 P2221 P 2c 2 17* P 2 2 21* P2221* P2221* P 21 2 17:cab P 21 2 2 P2122 P2122 P 2a 2a 17:bca P 2 21 2 P2212 P2212 P 2 2b 18 P 21 21 2 P21212 P21212 P 2 2ab 18:cab P 2 21 21 P22121 P22121 P 2bc 2 18:bca P 21 2 21 P21221 P21221 P 2ac 2ac 19 P 21 21 21 P212121 P212121 P 2ac 2ab 20 C 2 2 21 C2221 C2221 C 2c 2 20* C 2 2 21* C2221* C2221* C 21 2 20:cab A 21 2 2 A2122 A2122 A 2a 2a 20:cab* A 21 2 2* A2122* A2122* A 2a 21 20:bca B 2 21 2 B2212 B2212 B 2 2b 21 C 2 2 2 C222 C222 C 2 2 21:cab A 2 2 2 A222 A222 A 2 2 21:bca B 2 2 2 B222 B222 B 2 2 22 F 2 2 2 F222 F222 F 2 2 23 I 2 2 2 I222 I222 I 2 2 24 I 21 21 21 I212121 I212121 I 2b 2c 25 P m m 2 Pmm2 Pmm2 P 2 -2 25:cab P 2 m m P2mm P2mm P -2 2 25:bca P m 2 m Pm2m Pm2m P -2 -2 26 P m c 21 Pmc21 Pmc21 P 2c -2 26* P m c 21* Pmc21* Pmc21* P 21 -2 26:ba-c P c m 21 Pcm21 Pcm21 P 2c -2c 26:ba-c* P c m 21* Pcm21* Pcm21* P 21 -2c 26:cab P 21 m a P21ma P21ma P -2a 2a 26:-cba P 21 a m P21am P21am P -2 2a 26:bca P b 21 m Pb21m Pb21m P -2 -2b 26:a-cb P m 21 b Pm21b Pm21b P -2b -2 27 P c c 2 Pcc2 Pcc2 P 2 -2c 27:cab P 2 a a P2aa P2aa P -2a 2 27:bca P b 2 b Pb2b Pb2b P -2b -2b 28 P m a 2 Pma2 Pma2 P 2 -2a 28* P m a 2* Pma2* Pma2* P 2 -21 28:ba-c P b m 2 Pbm2 Pbm2 P 2 -2b 28:cab P 2 m b P2mb P2mb P -2b 2 28:-cba P 2 c m P2cm P2cm P -2c 2 28:-cba* P 2 c m* P2cm* P2cm* P -21 2 28:bca P c 2 m Pc2m Pc2m P -2c -2c 28:a-cb P m 2 a Pm2a Pm2a P -2a -2a 29 P c a 21 Pca21 Pca21 P 2c -2ac 29:ba-c P b c 21 Pbc21 Pbc21 P 2c -2b 29:cab P 21 a b P21ab P21ab P -2b 2a 29:-cba P 21 c a P21ca P21ca P -2ac 2a 29:bca P c 21 b Pc21b Pc21b P -2bc -2c 29:a-cb P b 21 a Pb21a Pb21a P -2a -2ab 30 P n c 2 Pnc2 Pnc2 P 2 -2bc 30:ba-c P c n 2 Pcn2 Pcn2 P 2 -2ac 30:cab P 2 n a P2na P2na P -2ac 2 30:-cba P 2 a n P2an P2an P -2ab 2 30:bca P b 2 n Pb2n Pb2n P -2ab -2a 30:a-cb P n 2 b Pn2b Pn2b P -2bc -2b 31 P m n 21 Pmn21 Pmn21 P 2ac -2 31:ba-c P n m 21 Pnm21 Pnm21 P 2bc -2bc 31:cab P 21 m n P21mn P21mn P -2ab 2ab 31:-cba P 21 n m P21nm P21nm P -2 2ac 31:bca P n 21 m Pn21m Pn21m P -2 -2bc 31:a-cb P m 21 n Pm21n Pm21n P -2ab -2 32 P b a 2 Pba2 Pba2 P 2 -2ab 32:cab P 2 c b P2cb P2cb P -2bc 2 32:bca P c 2 a Pc2a Pc2a P -2ac -2a 33 P n a 21 Pna21 Pna21 P 2c -2n 33* P n a 21* Pna21* Pna21* P 21 -2n 33:ba-c P b n 21 Pbn21 Pbn21 P 2c -2ab 33:ba-c* P b n 21* Pbn21* Pbn21* P 21 -2ab 33:cab P 21 n b P21nb P21nb P -2bc 2a 33:cab* P 21 n b* P21nb* P21nb* P -2bc 21 33:-cba P 21 c n P21cn P21cn P -2n 2a 33:-cba* P 21 c n* P21cn* P21cn* P -2n 21 33:bca P c 21 n Pc21n Pc21n P -2n -2ac 33:a-cb P n 21 a Pn21a Pn21a P -2ac -2n 34 P n n 2 Pnn2 Pnn2 P 2 -2n 34:cab P 2 n n P2nn P2nn P -2n 2 34:bca P n 2 n Pn2n Pn2n P -2n -2n 35 C m m 2 Cmm2 Cmm2 C 2 -2 35:cab A 2 m m A2mm A2mm A -2 2 35:bca B m 2 m Bm2m Bm2m B -2 -2 36 C m c 21 Cmc21 Cmc21 C 2c -2 36* C m c 21* Cmc21* Cmc21* C 21 -2 36:ba-c C c m 21 Ccm21 Ccm21 C 2c -2c 36:ba-c* C c m 21* Ccm21* Ccm21* C 21 -2c 36:cab A 21 m a A21ma A21ma A -2a 2a 36:cab* A 21 m a* A21ma* A21ma* A -2a 21 36:-cba A 21 a m A21am A21am A -2 2a 36:-cba* A 21 a m* A21am* A21am* A -2 21 36:bca B b 21 m Bb21m Bb21m B -2 -2b 36:a-cb B m 21 b Bm21b Bm21b B -2b -2 37 C c c 2 Ccc2 Ccc2 C 2 -2c 37:cab A 2 a a A2aa A2aa A -2a 2 37:bca B b 2 b Bb2b Bb2b B -2b -2b 38 A m m 2 Amm2 Amm2 A 2 -2 38:ba-c B m m 2 Bmm2 Bmm2 B 2 -2 38:cab B 2 m m B2mm B2mm B -2 2 38:-cba C 2 m m C2mm C2mm C -2 2 38:bca C m 2 m Cm2m Cm2m C -2 -2 38:a-cb A m 2 m Am2m Am2m A -2 -2 39 A b m 2 Abm2 Abm2 A 2 -2b 39:ba-c B m a 2 Bma2 Bma2 B 2 -2a 39:cab B 2 c m B2cm B2cm B -2a 2 39:-cba C 2 m b C2mb C2mb C -2a 2 39:bca C m 2 a Cm2a Cm2a C -2a -2a 39:a-cb A c 2 m Ac2m Ac2m A -2b -2b 40 A m a 2 Ama2 Ama2 A 2 -2a 40:ba-c B b m 2 Bbm2 Bbm2 B 2 -2b 40:cab B 2 m b B2mb B2mb B -2b 2 40:-cba C 2 c m C2cm C2cm C -2c 2 40:bca C c 2 m Cc2m Cc2m C -2c -2c 40:a-cb A m 2 a Am2a Am2a A -2a -2a 41 A b a 2 Aba2 Aba2 A 2 -2ab 41:ba-c B b a 2 Bba2 Bba2 B 2 -2ab 41:cab B 2 c b B2cb B2cb B -2ab 2 41:-cba C 2 c b C2cb C2cb C -2ac 2 41:bca C c 2 a Cc2a Cc2a C -2ac -2a 41:a-cb A c 2 a Ac2a Ac2a A -2ab -2a 42 F m m 2 Fmm2 Fmm2 F 2 -2 42:cab F 2 m m F2mm F2mm F -2 2 42:bca F m 2 m Fm2m Fm2m F -2 -2 43 F d d 2 Fdd2 Fdd2 F 2 -2d 43:cab F 2 d d F2dd F2dd F -2d 2 43:bca F d 2 d Fd2d Fd2d F -2d -2d 44 I m m 2 Imm2 Imm2 I 2 -2 44:cab I 2 m m I2mm I2mm I -2 2 44:bca I m 2 m Im2m Im2m I -2 -2 45 I b a 2 Iba2 Iba2 I 2 -2c 45:cab I 2 c b I2cb I2cb I -2a 2 45:bca I c 2 a Ic2a Ic2a I -2b -2b 46 I m a 2 Ima2 Ima2 I 2 -2a 46:ba-c I b m 2 Ibm2 Ibm2 I 2 -2b 46:cab I 2 m b I2mb I2mb I -2b 2 46:-cba I 2 c m I2cm I2cm I -2c 2 46:bca I c 2 m Ic2m Ic2m I -2c -2c 46:a-cb I m 2 a Im2a Im2a I -2a -2a 47 P m m m Pmmm Pmmm -P 2 2 48:1 P n n n Pnnn Pnnn P 2 2 -1n 48:2 P n n n Pnnn Pnnn -P 2ab 2bc 49 P c c m Pccm Pccm -P 2 2c 49:cab P m a a Pmaa Pmaa -P 2a 2 49:bca P b m b Pbmb Pbmb -P 2b 2b 50:1 P b a n Pban Pban P 2 2 -1ab 50:2 P b a n Pban Pban -P 2ab 2b 50:1cab P n c b Pncb Pncb P 2 2 -1bc 50:2cab P n c b Pncb Pncb -P 2b 2bc 50:1bca P c n a Pcna Pcna P 2 2 -1ac 50:2bca P c n a Pcna Pcna -P 2a 2c 51 P m m a Pmma Pmma -P 2a 2a 51:ba-c P m m b Pmmb Pmmb -P 2b 2 51:cab P b m m Pbmm Pbmm -P 2 2b 51:-cba P c m m Pcmm Pcmm -P 2c 2c 51:bca P m c m Pmcm Pmcm -P 2c 2 51:a-cb P m a m Pmam Pmam -P 2 2a 52 P n n a Pnna Pnna -P 2a 2bc 52:ba-c P n n b Pnnb Pnnb -P 2b 2n 52:cab P b n n Pbnn Pbnn -P 2n 2b 52:-cba P c n n Pcnn Pcnn -P 2ab 2c 52:bca P n c n Pncn Pncn -P 2ab 2n 52:a-cb P n a n Pnan Pnan -P 2n 2bc 53 P m n a Pmna Pmna -P 2ac 2 53:ba-c P n m b Pnmb Pnmb -P 2bc 2bc 53:cab P b m n Pbmn Pbmn -P 2ab 2ab 53:-cba P c n m Pcnm Pcnm -P 2 2ac 53:bca P n c m Pncm Pncm -P 2 2bc 53:a-cb P m a n Pman Pman -P 2ab 2 54 P c c a Pcca Pcca -P 2a 2ac 54:ba-c P c c b Pccb Pccb -P 2b 2c 54:cab P b a a Pbaa Pbaa -P 2a 2b 54:-cba P c a a Pcaa Pcaa -P 2ac 2c 54:bca P b c b Pbcb Pbcb -P 2bc 2b 54:a-cb P b a b Pbab Pbab -P 2b 2ab 55 P b a m Pbam Pbam -P 2 2ab 55:cab P m c b Pmcb Pmcb -P 2bc 2 55:bca P c m a Pcma Pcma -P 2ac 2ac 56 P c c n Pccn Pccn -P 2ab 2ac 56:cab P n a a Pnaa Pnaa -P 2ac 2bc 56:bca P b n b Pbnb Pbnb -P 2bc 2ab 57 P b c m Pbcm Pbcm -P 2c 2b 57:ba-c P c a m Pcam Pcam -P 2c 2ac 57:cab P m c a Pmca Pmca -P 2ac 2a 57:-cba P m a b Pmab Pmab -P 2b 2a 57:bca P b m a Pbma Pbma -P 2a 2ab 57:a-cb P c m b Pcmb Pcmb -P 2bc 2c 58 P n n m Pnnm Pnnm -P 2 2n 58:cab P m n n Pmnn Pmnn -P 2n 2 58:bca P n m n Pnmn Pnmn -P 2n 2n 59:1 P m m n Pmmn Pmmn P 2 2ab -1 59:2 P m m n Pmmn Pmmn -P 2ab 2a 59:1cab P n m m Pnmm Pnmm P 2bc 2 -1 59:2cab P n m m Pnmm Pnmm -P 2c 2bc 59:1bca P m n m Pmnm Pmnm P 2ac 2ac 59:2bca P m n m Pmnm Pmnm -P 2c 2a 60 P b c n Pbcn Pbcn -P 2n 2ab 60:ba-c P c a n Pcan Pcan -P 2n 2c 60:cab P n c a Pnca Pnca -P 2a 2n 60:-cba P n a b Pnab Pnab -P 2bc 2n 60:bca P b n a Pbna Pbna -P 2ac 2b 60:a-cb P c n b Pcnb Pcnb -P 2b 2ac 61 P b c a Pbca Pbca -P 2ac 2ab 61:ba-c P c a b Pcab Pcab -P 2bc 2ac 62 P n m a Pnma Pnma -P 2ac 2n 62:ba-c P m n b Pmnb Pmnb -P 2bc 2a 62:cab P b n m Pbnm Pbnm -P 2c 2ab 62:-cba P c m n Pcmn Pcmn -P 2n 2ac 62:bca P m c n Pmcn Pmcn -P 2n 2a 62:a-cb P n a m Pnam Pnam -P 2c 2n 63 C m c m Cmcm Cmcm -C 2c 2 63:ba-c C c m m Ccmm Ccmm -C 2c 2c 63:cab A m m a Amma Amma -A 2a 2a 63:-cba A m a m Amam Amam -A 2 2a 63:bca B b m m Bbmm Bbmm -B 2 2b 63:a-cb B m m b Bmmb Bmmb -B 2b 2 64 C m c a Cmca Cmca -C 2ac 2 64:ba-c C c m b Ccmb Ccmb -C 2ac 2ac 64:cab A b m a Abma Abma -A 2ab 2ab 64:-cba A c a m Acam Acam -A 2 2ab 64:bca B b c m Bbcm Bbcm -B 2 2ab 64:a-cb B m a b Bmab Bmab -B 2ab 2 65 C m m m Cmmm Cmmm -C 2 2 65:cab A m m m Ammm Ammm -A 2 2 65:bca B m m m Bmmm Bmmm -B 2 2 66 C c c m Cccm Cccm -C 2 2c 66:cab A m a a Amaa Amaa -A 2a 2 66:bca B b m b Bbmb Bbmb -B 2b 2b 67 C m m a Cmma Cmma -C 2a 2 67:ba-c C m m b Cmmb Cmmb -C 2a 2a 67:cab A b m m Abmm Abmm -A 2b 2b 67:-cba A c m m Acmm Acmm -A 2 2b 67:bca B m c m Bmcm Bmcm -B 2 2a 67:a-cb B m a m Bmam Bmam -B 2a 2 68:1 C c c a Ccca Ccca C 2 2 -1ac 68:2 C c c a Ccca Ccca -C 2a 2ac 68:1ba-c C c c b Cccb Cccb C 2 2 -1ac 68:2ba-c C c c b Cccb Cccb -C 2a 2c 68:1cab A b a a Abaa Abaa A 2 2 -1ab 68:2cab A b a a Abaa Abaa -A 2a 2b 68:1-cba A c a a Acaa Acaa A 2 2 -1ab 68:2-cba A c a a Acaa Acaa -A 2ab 2b 68:1bca B b c b Bbcb Bbcb B 2 2 -1ab 68:2bca B b c b Bbcb Bbcb -B 2ab 2b 68:1a-cb B b a b Bbab Bbab B 2 2 -1ab 68:2a-cb B b a b Bbab Bbab -B 2b 2ab 69 F m m m Fmmm Fmmm -F 2 2 70:1 F d d d Fddd Fddd F 2 2 -1d 70:2 F d d d Fddd Fddd -F 2uv 2vw 71 I m m m Immm Immm -I 2 2 72 I b a m Ibam Ibam -I 2 2c 72:cab I m c b Imcb Imcb -I 2a 2 72:bca I c m a Icma Icma -I 2b 2b 73 I b c a Ibca Ibca -I 2b 2c 73:ba-c I c a b Icab Icab -I 2a 2b 74 I m m a Imma Imma -I 2b 2 74:ba-c I m m b Immb Immb -I 2a 2a 74:cab I b m m Ibmm Ibmm -I 2c 2c 74:-cba I c m m Icmm Icmm -I 2 2b 74:bca I m c m Imcm Imcm -I 2 2a 74:a-cb I m a m Imam Imam -I 2c 2 75 P 4 P4 P4 P 4 76 P 41 P41 P41 P 4w 76* P 41* P41* P41* P 41 77 P 42 P42 P42 P 4c 77* P 42* P42* P42* P 42 78 P 43 P43 P43 P 4cw 78* P 43* P43* P43* P 43 79 I 4 I4 I4 I 4 80 I 41 I41 I41 I 4bw 81 P -4 P-4 P-4 P -4 82 I -4 I-4 I-4 I -4 83 P 4/m P4/m P4/m -P 4 84 P 42/m P42/m P42/m -P 4c 84* P 42/m* P42/m* P42/m* -P 42 85:1 P 4/n P4/n P4/n P 4ab -1ab 85:2 P 4/n P4/n P4/n -P 4a 86:1 P 42/n P42/n P42/n P 4n -1n 86:2 P 42/n P42/n P42/n -P 4bc 87 I 4/m I4/m I4/m -I 4 88:1 I 41/a I41/a I41/a I 4bw -1bw 88:2 I 41/a I41/a I41/a -I 4ad 89 P 4 2 2 P422 P422 P 4 2 90 P 4 21 2 P4212 P4212 P 4ab 2ab 91 P 41 2 2 P4122 P4122 P 4w 2c 91* P 41 2 2* P4122* P4122* P 41 2c 92 P 41 21 2 P41212 P41212 P 4abw 2nw 93 P 42 2 2 P4222 P4222 P 4c 2 93* P 42 2 2* P4222* P4222* P 42 2 94 P 42 21 2 P42212 P42212 P 4n 2n 95 P 43 2 2 P4322 P4322 P 4cw 2c 95* P 43 2 2* P4322* P4322* P 43 2c 96 P 43 21 2 P43212 P43212 P 4nw 2abw 97 I 4 2 2 I422 I422 I 4 2 98 I 41 2 2 I4122 I4122 I 4bw 2bw 99 P 4 m m P4mm P4mm P 4 -2 100 P 4 b m P4bm P4bm P 4 -2ab 101 P 42 c m P42cm P42cm P 4c -2c 101* P 42 c m* P42cm* P42cm* P 42 -2c 102 P 42 n m P42nm P42nm P 4n -2n 103 P 4 c c P4cc P4cc P 4 -2c 104 P 4 n c P4nc P4nc P 4 -2n 105 P 42 m c P42mc P42mc P 4c -2 105* P 42 m c* P42mc* P42mc* P 42 -2 106 P 42 b c P42bc P42bc P 4c -2ab 106* P 42 b c* P42bc* P42bc* P 42 -2ab 107 I 4 m m I4mm I4mm I 4 -2 108 I 4 c m I4cm I4cm I 4 -2c 109 I 41 m d I41md I41md I 4bw -2 110 I 41 c d I41cd I41cd I 4bw -2c 111 P -4 2 m P-42m P-42m P -4 2 112 P -4 2 c P-42c P-42c P -4 2c 113 P -4 21 m P-421m P-421m P -4 2ab 114 P -4 21 c P-421c P-421c P -4 2n 115 P -4 m 2 P-4m2 P-4m2 P -4 -2 116 P -4 c 2 P-4c2 P-4c2 P -4 -2c 117 P -4 b 2 P-4b2 P-4b2 P -4 -2ab 118 P -4 n 2 P-4n2 P-4n2 P -4 -2n 119 I -4 m 2 I-4m2 I-4m2 I -4 -2 120 I -4 c 2 I-4c2 I-4c2 I -4 -2c 121 I -4 2 m I-42m I-42m I -4 2 122 I -4 2 d I-42d I-42d I -4 2bw 123 P 4/m m m P4/mmm P4/mmm -P 4 2 124 P 4/m c c P4/mcc P4/mcc -P 4 2c 125:1 P 4/n b m P4/nbm P4/nbm P 4 2 -1ab 125:2 P 4/n b m P4/nbm P4/nbm -P 4a 2b 126:1 P 4/n n c P4/nnc P4/nnc P 4 2 -1n 126:2 P 4/n n c P4/nnc P4/nnc -P 4a 2bc 127 P 4/m b m P4/mbm P4/mbm -P 4 2ab 128 P 4/m n c P4/mnc P4/mnc -P 4 2n 129:1 P 4/n m m P4/nmm P4/nmm P 4ab 2ab 129:2 P 4/n m m P4/nmm P4/nmm -P 4a 2a 130:1 P 4/n c c P4/ncc P4/ncc P 4ab 2n - 130:2 P 4/n c c P4/ncc P4/ncc -P 4a 2ac 131 P 42/m m c P42/mmc P42/mmc -P 4c 2 132 P 42/m c m P42/mcm P42/mcm -P 4c 2c 133:1 P 42/n b c P42/nbc P42/nbc P 4n 2c -1 133:2 P 42/n b c P42/nbc P42/nbc -P 4ac 2b 134:1 P 42/n n m P42/nnm P42/nnm P 4n 2 -1n 134:2 P 42/n n m P42/nnm P42/nnm -P 4ac 2bc 135 P 42/m b c P42/mbc P42/mbc -P 4c 2ab 135* P 42/m b c* P42/mbc* P42/mbc* -P 42 2ab 136 P 42/m n m P42/mnm P42/mnm -P 4n 2n 137:1 P 42/n m c P42/nmc P42/nmc P 4n 2n -1 137:2 P 42/n m c P42/nmc P42/nmc -P 4ac 2a 138:1 P 42/n c m P42/ncm P42/ncm P 4n 2ab - 138:2 P 42/n c m P42/ncm P42/ncm -P 4ac 2ac 139 I 4/m m m I4/mmm I4/mmm -I 4 2 140 I 4/m c m I4/mcm I4/mcm -I 4 2c 141:1 I 41/a m d I41/amd I41/amd I 4bw 2bw 141:2 I 41/a m d I41/amd I41/amd -I 4bd 2 142:1 I 41/a c d I41/acd I41/acd I 4bw 2aw 142:2 I 41/a c d I41/acd I41/acd -I 4bd 2c 143 P 3 P3 P3 P 3 144 P 31 P31 P31 P 31 145 P 32 P32 P32 P 32 146:h R 3 R3 R3 R 3 146:r R 3 R3 R3 P 3* 147 P -3 P-3 P-3 -P 3 148:h R -3 R-3 R-3 -R 3 148:r R -3 R-3 R-3 -P 3* 149 P 3 1 2 P312 P32 P 3 2 150 P 3 2 1 P321 P32 P 3 2 151 P 31 1 2 P3112 P312 P 31 2 (0 152 P 31 2 1 P3121 P312 P 31 2 153 P 32 1 2 P3212 P322 P 32 2 (0 154 P 32 2 1 P3221 P322 P 32 2 155:h R 3 2 R32 R32 R 3 2 155:r R 3 2 R32 R32 P 3* 2 156 P 3 m 1 P3m1 P3m P 3 -2" 157 P 3 1 m P31m P3m P 3 -2 158 P 3 c 1 P3c1 P3c P 3 -2"c 159 P 3 1 c P31c P3c P 3 -2c 160:h R 3 m R3m R3m R 3 -2 160:r R 3 m R3m R3m P 3* -2 161:h R 3 c R3c R3c R 3 -2"c 161:r R 3 c R3c R3c P 3* -2n 162 P -3 1 m P-31m P-3m -P 3 2 163 P -3 1 c P-31c P-3c -P 3 2c 164 P -3 m 1 P-3m1 P-3m -P 3 2" 165 P -3 c 1 P-3c1 P-3c -P 3 2"c 166:h R -3 m R-3m R-3m -R 3 2" 166:r R -3 m R-3m R-3m -P 3* 2 167:h R -3 c R-3c R-3c -R 3 2"c 167:r R -3 c R-3c R-3c -P 3* 2n 168 P 6 P6 P6 P 6 169 P 61 P61 P61 P 61 170 P 65 P65 P65 P 65 171 P 62 P62 P62 P 62 172 P 64 P64 P64 P 64 173 P 63 P63 P63 P 6c 173* P 63* P63* P63* P 63 174 P -6 P-6 P-6 P -6 175 P 6/m P6/m P6/m -P 6 176 P 63/m P63/m P63/m -P 6c 176* P 63/m* P63/m* P63/m* -P 63 177 P 6 2 2 P622 P622 P 6 2 178 P 61 2 2 P6122 P6122 P 61 2 (0 0 5) 179 P 65 2 2 P6522 P6522 P 65 2 (0 0 1) 180 P 62 2 2 P6222 P6222 P 62 2 (0 0 4) 181 P 64 2 2 P6422 P6422 P 64 2 (0 0 2) 182 P 63 2 2 P6322 P6322 P 6c 2c 182* P 63 2 2* P6322* P6322* P 63 2c 183 P 6 m m P6mm P6mm P 6 -2 184 P 6 c c P6cc P6cc P 6 -2c 185 P 63 c m P63cm P63cm P 6c -2 185* P 63 c m* P63cm* P63cm* P 63 -2 186 P 63 m c P63mc P63mc P 6c -2c 186* P 63 m c* P63mc* P63mc* P 63 -2c 187 P -6 m 2 P-6m2 P-6m2 P -6 2 188 P -6 c 2 P-6c2 P-6c2 P -6c 2 189 P -6 2 m P-62m P-62m P -6 -2 190 P -6 2 c P-62c P-62c P -6c -2c 191 P 6/m m m P6/mmm P6/mmm -P 6 2 192 P 6/m c c P6/mcc P6/mcc -P 6 2c 193 P 63/m c m P63/mcm P63/mcm -P 6c 2 193* P 63/m c m* P63/mcm* P63/mcm* -P 63 2 194 P 63/m m c P63/mmc P63/mmc -P 6c 2c 194* P 63/m m c* P63/mmc* P63/mmc* -P 63 2c 195 P 2 3 P23 P23 P 2 2 3 196 F 2 3 F23 F23 F 2 2 3 197 I 2 3 I23 I23 I 2 2 3 198 P 21 3 P213 P213 P 2ac 2ab 3 199 I 21 3 I213 I213 I 2b 2c 3 200 P m -3 Pm-3 Pm-3 -P 2 2 3 201:1 P n -3 Pn-3 Pn-3 P 2 2 3 -1n 201:2 P n -3 Pn-3 Pn-3 -P 2ab 2bc 3 202 F m -3 Fm-3 Fm-3 -F 2 2 3 203:1 F d -3 Fd-3 Fd-3 F 2 2 3 -1d 203:2 F d -3 Fd-3 Fd-3 -F 2uv 2vw 3 204 I m -3 Im-3 Im-3 -I 2 2 3 205 P a -3 Pa-3 Pa-3 -P 2ac 2ab 3 206 I a -3 Ia-3 Ia-3 -I 2b 2c 3 207 P 4 3 2 P432 P432 P 4 2 3 208 P 42 3 2 P4232 P4232 P 4n 2 3 209 F 4 3 2 F432 F432 F 4 2 3 210 F 41 3 2 F4132 F4132 F 4d 2 3 211 I 4 3 2 I432 I432 I 4 2 3 212 P 43 3 2 P4332 P4332 P 4acd 2ab 3 213 P 41 3 2 P4132 P4132 P 4bd 2ab 3 214 I 41 3 2 I4132 I4132 I 4bd 2c 3 215 P -4 3 m P-43m P-43m P -4 2 3 216 F -4 3 m F-43m F-43m F -4 2 3 217 I -4 3 m I-43m I-43m I -4 2 3 218 P -4 3 n P-43n P-43n P -4n 2 3 219 F -4 3 c F-43c F-43c F -4a 2 3 220 I -4 3 d I-43d I-43d I -4bd 2c 3 221 P m -3 m Pm-3m Pm-3m -P 4 2 3 222:1 P n -3 n Pn-3n Pn-3n P 4 2 3 -1n 222:2 P n -3 n Pn-3n Pn-3n -P 4a 2bc 3 223 P m -3 n Pm-3n Pm-3n -P 4n 2 3 224:1 P n -3 m Pn-3m Pn-3m P 4n 2 3 -1n 224:2 P n -3 m Pn-3m Pn-3m -P 4bc 2bc 3 225 F m -3 m Fm-3m Fm-3m -F 4 2 3 226 F m -3 c Fm-3c Fm-3c -F 4a 2 3 227:1 F d -3 m Fd-3m Fd-3m F 4d 2 3 -1d 227:2 F d -3 m Fd-3m Fd-3m -F 4vw 2vw 3 228:1 F d -3 c Fd-3c Fd-3c F 4d 2 3 -1ad 228:2 F d -3 c Fd-3c Fd-3c -F 4ud 2vw 3 229 I m -3 m Im-3m Im-3m -I 4 2 3 230 I a -3 d Ia-3d Ia-3d -I 4bd 2c 3 */ // primitives: // 1: primitive: 1. P1 2. P1¯, // 3. P2 10. P2/m // 4. P21 11. P21/m // 6. Pm 13. P2/c // 7. Pc 14. P21/c // 16. P222 25. Pmm2 29. Pca21 33. Pna21 50. Pban 54. Pcca 58. Pnnm 62. Pnma // 17. P2221 26. Pmc21 30. Pnc2 34. Pnn2 51. Pmma 55. Pbam 59. Pmmn // 18. P21212 27. Pcc2 31. Pmn21 47. Pmmm 52. Pnna 56. Pccn 60. Pbcn // 19. P212121 28. Pma2 32. Pba2 49. Pccm 53. Pmna 57. Pbcm 61. Pbca // 75. P4 81. P4¯ 86. P42/n 92. P41212 96. P43212 102. P42nm 106. P42bc 114. P4_21c 118. P4¯n2 126. P4/nnc 130. P4/ncc 134. P42/nnm 138. P42/ncm // 76. P41 83. P4/m 89. P422 93. P4222 99. P4mm 103. P4cc 111. P4¯2m 115. P4¯m2 123. P4/mmm 127. P4/mbm 131. P42/mmc 135. P42/mbc // 77. P42 84. P42/m 90. P4212 94. P42212 100. P4bm 104. P4nc 112. P4¯2c 116. P4¯c2 124. P4/mcc 128. P4/mnc 132. P42/mcm 136. P42/mnm // 78. P43 85. P4/n 91. P4122 95. P4322 101. P42cm 105. P42mc 113. P4¯21m 117. P4¯b2 125. P4/nbm 129. P4/nmm 133. P42/nbc 137. P42/nmc // // + all hexagonal and rhombohedral // 2: base-centered: 5. C2 8. Cm 9. Cc 12. C2/m 15. C2/c // 20. C2221 37. Ccc2 66. Cccm // 21. C222 63. Cmcm 67. Cmma // 35. Cmm2 64. Cmca 68. Ccca // 36. Cmc21 65. Cmmm // 3: face-centered: 22. F222 42. Fmm2 43. Fdd2 69. Fmmm 70. Fddd // 143. P3 149. P312 153. P3212 158. P3c1 164. P3¯m1 // 144. P31 150. P321 154. P3221 159. P31c 165. P3¯c1 // 145. P32 151. P3112 156. P3m1 162. P3¯1m // 147. P3¯ 152. P3121 157. P31m 163. P3¯1c // 4: body-centered: 80. I41 97. I422 109. I41md 121. I4¯2m 141. I41/amd // 82. I4¯ 98. I4122 110. I41cd 122. I4¯2d 142. I41/acd // 87. I4/m 107. I4mm 119. I4¯m2 139. I4/mmm // 88. I41/a 108. I4cm 120. I4¯c2 140. I4/mcm /** * intlNo:options;nOps;schoenflies;hermannMauguin;Hall;BilbaoFlag * * 530 settings, some with multiple names */ // intlNo:options;nOps;schoenflies;hermannMauguin;Hall;BilbaoFlag // 0 1 2 3 4 5 // the 5th term is not actually checked; we have ";-b" as 5th term right now for "not Bilbao" // "48:1;8;d2h^2;p n n n:1;p 2 2 -1n;-b", // and is probably origin choice 1. // * indicates a nonstandard Hall name "p 21" same as "p 2yb" (removed in 16.2.28) // (this was some idea that Sid Hall gave me by email, but it no // longer seems to matter, and it caused trouble with modelkit assign spacegroup // 4:c*;2;c2^2;p 1 1 21*;p 21 // added # of operators to help in search phase // "4:b;2;c2^2;p 1 21 1;p 2yb", //full name //610 settings for 230 space groups (608 from ITA; 2 for added 152 and 154 c-shifts //including also several duplicates // private static String[] STR_SG = { "1;1.1;;1;c1^1;p 1;p 1", "2;2.1;;2;ci^1;p -1;-p 1", "3:b;3.1;;2;c2^1;p 1 2 1;p 2y", //full name "3:b;3.1;;2;c2^1;p 2;p 2y", "3:c;3.2;c,a,b;2;c2^1;p 1 1 2;p 2", "3:a;3.3;b,c,a;2;c2^1;p 2 1 1;p 2x", "4:b;4.1;;2;c2^2;p 1 21 1;p 2yb", //full name "4:b;4.1;;2;c2^2;p 21;p 2yb", //"4:b*;4.1;;2;c2^2;p 1 21 1*;p 2y1", //nonstandard "4:c;4.2;c,a,b;2;c2^2;p 1 1 21;p 2c", //"4:c*;4.2;c,a,b;2;c2^2;p 1 1 21*;p 21", //nonstandard "4:a;4.3;b,c,a;2;c2^2;p 21 1 1;p 2xa", //"4:a*;4.3;b,c,a;2;c2^2;p 21 1 1*;p 2x1", //nonstandard "5:b1;5.1;;4;c2^3;c 1 2 1;c 2y", //full name "5:b1;5.1;;4;c2^3;c 2;c 2y", "5:b2;5.2;-a-c,b,a;4;c2^3;a 1 2 1;a 2y", "5:b3;5.3;c,b,-a-c;4;c2^3;i 1 2 1;i 2y", "5:c1;5.4;c,a,b;4;c2^3;a 1 1 2;a 2", "5:c2;5.5;a,-a-c,b;4;c2^3;b 1 1 2;b 2", "5:c3;5.6;-a-c,c,b;4;c2^3;i 1 1 2;i 2", "5:a1;5.7;b,c,a;4;c2^3;b 2 1 1;b 2x", "5:a2;5.8;b,a,-a-c;4;c2^3;c 2 1 1;c 2x", "5:a3;5.9;b,-a-c,c;4;c2^3;i 2 1 1;i 2x", "6:b;6.1;;2;cs^1;p 1 m 1;p -2y", //full name "6:b;6.1;;2;cs^1;p m;p -2y", "6:c;6.2;c,a,b;2;cs^1;p 1 1 m;p -2", "6:a;6.3;b,c,a;2;cs^1;p m 1 1;p -2x", "7:b1;7.1;;2;cs^2;p 1 c 1;p -2yc", //full name "7:b1;7.1;;2;cs^2;p c;p -2yc", "7:b2;7.2;-a-c,b,a;2;cs^2;p 1 n 1;p -2yac", //full name "7:b2;7.2;-a-c,b,a;2;cs^2;p n;p -2yac", "7:b3;7.3;c,b,-a-c;2;cs^2;p 1 a 1;p -2ya", //full name "7:b3;7.3;c,b,-a-c;2;cs^2;p a;p -2ya", "7:c1;7.4;c,a,b;2;cs^2;p 1 1 a;p -2a", "7:c2;7.5;a,-a-c,b;2;cs^2;p 1 1 n;p -2ab", "7:c3;7.6;-a-c,c,b;2;cs^2;p 1 1 b;p -2b", "7:a1;7.7;b,c,a;2;cs^2;p b 1 1;p -2xb", "7:a2;7.8;b,a,-a-c;2;cs^2;p n 1 1;p -2xbc", "7:a3;7.9;b,-a-c,c;2;cs^2;p c 1 1;p -2xc", "8:b1;8.1;;4;cs^3;c 1 m 1;c -2y", //full name "8:b1;8.1;;4;cs^3;c m;c -2y", "8:b2;8.2;-a-c,b,a;4;cs^3;a 1 m 1;a -2y", "8:b3;8.3;c,b,-a-c;4;cs^3;i 1 m 1;i -2y", //full name "8:b3;8.3;c,b,-a-c;4;cs^3;i m;i -2y", "8:c1;8.4;c,a,b;4;cs^3;a 1 1 m;a -2", "8:c2;8.5;a,-a-c,b;4;cs^3;b 1 1 m;b -2", "8:c3;8.6;-a-c,c,b;4;cs^3;i 1 1 m;i -2", "8:a1;8.7;b,c,a;4;cs^3;b m 1 1;b -2x", "8:a2;8.8;b,a,-a-c;4;cs^3;c m 1 1;c -2x", "8:a3;8.9;b,-a-c,c;4;cs^3;i m 1 1;i -2x", "9:b1;9.1;;4;cs^4;c 1 c 1;c -2yc", //full name "9:b1;9.1;;4;cs^4;c c;c -2yc", "9:b2;9.2;-a-c,b,a;4;cs^4;a 1 n 1;a -2yab", "9:b3;9.3;c,b,-a-c;4;cs^4;i 1 a 1;i -2ya", "9:-b1;9.4;c,-b,a;4;cs^4;a 1 a 1;a -2ya", "9:-b2;9.5;a,-b,-a-c;4;cs^4;c 1 n 1;c -2yac", "9:-b3;9.6;-a-c,-b,c;4;cs^4;i 1 c 1;i -2yc", "9:c1;9.7;c,a,b;4;cs^4;a 1 1 a;a -2a", "9:c2;9.8;a,-a-c,b;4;cs^4;b 1 1 n;b -2ab", "9:c3;9.9;-a-c,c,b;4;cs^4;i 1 1 b;i -2b", "9:-c1;9.10;a,c,-b;4;cs^4;b 1 1 b;b -2b", "9:-c2;9.11;-a-c,a,-b;4;cs^4;a 1 1 n;a -2ab", "9:-c3;9.12;c,-a-c,-b;4;cs^4;i 1 1 a;i -2a", "9:a1;9.13;b,c,a;4;cs^4;b b 1 1;b -2xb", "9:a2;9.14;b,a,-a-c;4;cs^4;c n 1 1;c -2xac", "9:a3;9.15;b,-a-c,c;4;cs^4;i c 1 1;i -2xc", "9:-a1;9.16;-b,a,c;4;cs^4;c c 1 1;c -2xc", "9:-a2;9.17;-b,-a-c,a;4;cs^4;b n 1 1;b -2xab", "9:-a3;9.18;-b,c,-a-c;4;cs^4;i b 1 1;i -2xb", "10:b;10.1;;4;c2h^1;p 1 2/m 1;-p 2y", //full name "10:b;10.1;;4;c2h^1;p 2/m;-p 2y", "10:c;10.2;c,a,b;4;c2h^1;p 1 1 2/m;-p 2", "10:a;10.3;b,c,a;4;c2h^1;p 2/m 1 1;-p 2x", "11:b;11.1;;4;c2h^2;p 1 21/m 1;-p 2yb", //full name "11:b;11.1;;4;c2h^2;p 21/m;-p 2yb", //"11:b*;11.1;;4;c2h^2;p 1 21/m 1*;-p 2y1", //nonstandard "11:c;11.2;c,a,b;4;c2h^2;p 1 1 21/m;-p 2c", //"11:c*;11.2;c,a,b;4;c2h^2;p 1 1 21/m*;-p 21", //nonstandard "11:a;11.3;b,c,a;4;c2h^2;p 21/m 1 1;-p 2xa", //"11:a*;11.3;b,c,a;4;c2h^2;p 21/m 1 1*;-p 2x1", //nonstandard "12:b1;12.1;;8;c2h^3;c 1 2/m 1;-c 2y", //full name "12:b1;12.1;;8;c2h^3;c 2/m;-c 2y", "12:b2;12.2;-a-c,b,a;8;c2h^3;a 1 2/m 1;-a 2y", "12:b3;12.3;c,b,-a-c;8;c2h^3;i 1 2/m 1;-i 2y", //full name "12:b3;12.3;c,b,-a-c;8;c2h^3;i 2/m;-i 2y", "12:c1;12.4;c,a,b;8;c2h^3;a 1 1 2/m;-a 2", "12:c2;12.5;a,-a-c,b;8;c2h^3;b 1 1 2/m;-b 2", "12:c3;12.6;-a-c,c,b;8;c2h^3;i 1 1 2/m;-i 2", "12:a1;12.7;b,c,a;8;c2h^3;b 2/m 1 1;-b 2x", "12:a2;12.8;b,a,-a-c;8;c2h^3;c 2/m 1 1;-c 2x", "12:a3;12.9;b,-a-c,c;8;c2h^3;i 2/m 1 1;-i 2x", "13:b1;13.1;;4;c2h^4;p 1 2/c 1;-p 2yc", //full name "13:b1;13.1;;4;c2h^4;p 2/c;-p 2yc", "13:b2;13.2;-a-c,b,a;4;c2h^4;p 1 2/n 1;-p 2yac", //full name "13:b2;13.2;-a-c,b,a;4;c2h^4;p 2/n;-p 2yac", "13:b3;13.3;c,b,-a-c;4;c2h^4;p 1 2/a 1;-p 2ya", //full name "13:b3;13.3;c,b,-a-c;4;c2h^4;p 2/a;-p 2ya", "13:c1;13.4;c,a,b;4;c2h^4;p 1 1 2/a;-p 2a", "13:c2;13.5;a,-a-c,b;4;c2h^4;p 1 1 2/n;-p 2ab", "13:c3;13.6;-a-c,c,b;4;c2h^4;p 1 1 2/b;-p 2b", "13:a1;13.7;b,c,a;4;c2h^4;p 2/b 1 1;-p 2xb", "13:a2;13.8;b,a,-a-c;4;c2h^4;p 2/n 1 1;-p 2xbc", "13:a3;13.9;b,-a-c,c;4;c2h^4;p 2/c 1 1;-p 2xc", "14:b1;14.1;;4;c2h^5;p 1 21/c 1;-p 2ybc", //full name "14:b1;14.1;;4;c2h^5;p 21/c;-p 2ybc", "14:b2;14.2;-a-c,b,a;4;c2h^5;p 1 21/n 1;-p 2yn", //full name "14:b2;14.2;-a-c,b,a;4;c2h^5;p 21/n;-p 2yn", "14:b3;14.3;c,b,-a-c;4;c2h^5;p 1 21/a 1;-p 2yab", //full name "14:b3;14.3;c,b,-a-c;4;c2h^5;p 21/a;-p 2yab", "14:c1;14.4;c,a,b;4;c2h^5;p 1 1 21/a;-p 2ac", "14:c2;14.5;a,-a-c,b;4;c2h^5;p 1 1 21/n;-p 2n", "14:c3;14.6;-a-c,c,b;4;c2h^5;p 1 1 21/b;-p 2bc", "14:a1;14.7;b,c,a;4;c2h^5;p 21/b 1 1;-p 2xab", "14:a2;14.8;b,a,-a-c;4;c2h^5;p 21/n 1 1;-p 2xn", "14:a3;14.9;b,-a-c,c;4;c2h^5;p 21/c 1 1;-p 2xac", "15:b1;15.1;;8;c2h^6;c 1 2/c 1;-c 2yc", //full name "15:b1;15.1;;8;c2h^6;c 2/c;-c 2yc", "15:b2;15.2;-a-c,b,a;8;c2h^6;a 1 2/n 1;-a 2yab", "15:b3;15.3;c,b,-a-c;8;c2h^6;i 1 2/a 1;-i 2ya", //full name "15:b3;15.3;c,b,-a-c;8;c2h^6;i 2/a;-i 2ya", "15:-b1;15.4;c,-b,a;8;c2h^6;a 1 2/a 1;-a 2ya", "15:-b2;15.5;a,-b,-a-c;8;c2h^6;c 1 2/n 1;-c 2yac", //full name "15:-b2;15.5;a,-b,-a-c;8;c2h^6;c 2/n;-c 2yac", "15:-b3;15.6;-a-c,-b,c;8;c2h^6;i 1 2/c 1;-i 2yc", //full name "15:-b3;15.6;-a-c,-b,c;8;c2h^6;i 2/c;-i 2yc", "15:c1;15.7;c,a,b;8;c2h^6;a 1 1 2/a;-a 2a", "15:c2;15.8;a,-a-c,b;8;c2h^6;b 1 1 2/n;-b 2ab", "15:c3;15.9;-a-c,c,b;8;c2h^6;i 1 1 2/b;-i 2b", "15:-c1;15.10;a,c,-b;8;c2h^6;b 1 1 2/b;-b 2b", "15:-c2;15.11;-a-c,a,-b;8;c2h^6;a 1 1 2/n;-a 2ab", "15:-c3;15.12;c,-a-c,-b;8;c2h^6;i 1 1 2/a;-i 2a", "15:a1;15.13;b,c,a;8;c2h^6;b 2/b 1 1;-b 2xb", "15:a2;15.14;b,a,-a-c;8;c2h^6;c 2/n 1 1;-c 2xac", "15:a3;15.15;b,-a-c,c;8;c2h^6;i 2/c 1 1;-i 2xc", "15:-a1;15.16;-b,a,c;8;c2h^6;c 2/c 1 1;-c 2xc", "15:-a2;15.17;-b,-a-c,a;8;c2h^6;b 2/n 1 1;-b 2xab", "15:-a3;15.18;-b,c,-a-c;8;c2h^6;i 2/b 1 1;-i 2xb", "16;16.1;;4;d2^1;p 2 2 2;p 2 2", "17;17.1;;4;d2^2;p 2 2 21;p 2c 2", //"17*;17.1;;4;d2^2;p 2 2 21*;p 21 2", //nonstandard "17:cab;17.2;c,a,b;4;d2^2;p 21 2 2;p 2a 2a", "17:bca;17.3;b,c,a;4;d2^2;p 2 21 2;p 2 2b", "18;18.1;;4;d2^3;p 21 21 2;p 2 2ab", "18:cab;18.2;c,a,b;4;d2^3;p 2 21 21;p 2bc 2", "18:bca;18.3;b,c,a;4;d2^3;p 21 2 21;p 2ac 2ac", "19;19.1;;4;d2^4;p 21 21 21;p 2ac 2ab", "20;20.1;;8;d2^5;c 2 2 21;c 2c 2", //"20*;20.1;;8;d2^5;c 2 2 21*;c 21 2", //nonstandard "20:cab;20.2;c,a,b;8;d2^5;a 21 2 2;a 2a 2a", "20:cab*;20.2;c,a,b;8;d2^5;a 21 2 2*;a 2a 21", //nonstandard "20:bca;20.3;b,c,a;8;d2^5;b 2 21 2;b 2 2b", "21;21.1;;8;d2^6;c 2 2 2;c 2 2", "21:cab;21.2;c,a,b;8;d2^6;a 2 2 2;a 2 2", "21:bca;21.3;b,c,a;8;d2^6;b 2 2 2;b 2 2", "22;22.1;;16;d2^7;f 2 2 2;f 2 2", "23;23.1;;8;d2^8;i 2 2 2;i 2 2", "24;24.1;;8;d2^9;i 21 21 21;i 2b 2c", "25;25.1;;4;c2v^1;p m m 2;p 2 -2", "25:cab;25.2;c,a,b;4;c2v^1;p 2 m m;p -2 2", "25:bca;25.3;b,c,a;4;c2v^1;p m 2 m;p -2 -2", "26;26.1;;4;c2v^2;p m c 21;p 2c -2", //"26*;26.1;;4;c2v^2;p m c 21*;p 21 -2", //nonstandard "26:ba-c;26.2;b,a,-c;4;c2v^2;p c m 21;p 2c -2c", "26:ba-c*;26.2;b,a,-c;4;c2v^2;p c m 21*;p 21 -2c", //nonstandard "26:cab;26.3;c,a,b;4;c2v^2;p 21 m a;p -2a 2a", "26:-cba;26.4;-c,b,a;4;c2v^2;p 21 a m;p -2 2a", "26:bca;26.5;b,c,a;4;c2v^2;p b 21 m;p -2 -2b", "26:a-cb;26.6;a,-c,b;4;c2v^2;p m 21 b;p -2b -2", "27;27.1;;4;c2v^3;p c c 2;p 2 -2c", "27:cab;27.2;c,a,b;4;c2v^3;p 2 a a;p -2a 2", "27:bca;27.3;b,c,a;4;c2v^3;p b 2 b;p -2b -2b", "28;28.1;;4;c2v^4;p m a 2;p 2 -2a", //"28*;28.1;;4;c2v^4;p m a 2*;p 2 -21", //nonstandard "28:ba-c;28.2;b,a,-c;4;c2v^4;p b m 2;p 2 -2b", "28:cab;28.3;c,a,b;4;c2v^4;p 2 m b;p -2b 2", "28:-cba;28.4;-c,b,a;4;c2v^4;p 2 c m;p -2c 2", "28:-cba*;28.4;-c,b,a;4;c2v^4;p 2 c m*;p -21 2", //nonstandard "28:bca;28.5;b,c,a;4;c2v^4;p c 2 m;p -2c -2c", "28:a-cb;28.6;a,-c,b;4;c2v^4;p m 2 a;p -2a -2a", "29;29.1;;4;c2v^5;p c a 21;p 2c -2ac", "29:ba-c;29.2;b,a,-c;4;c2v^5;p b c 21;p 2c -2b", "29:cab;29.3;c,a,b;4;c2v^5;p 21 a b;p -2b 2a", "29:-cba;29.4;-c,b,a;4;c2v^5;p 21 c a;p -2ac 2a", "29:bca;29.5;b,c,a;4;c2v^5;p c 21 b;p -2bc -2c", "29:a-cb;29.6;a,-c,b;4;c2v^5;p b 21 a;p -2a -2ab", "30;30.1;;4;c2v^6;p n c 2;p 2 -2bc", "30:ba-c;30.2;b,a,-c;4;c2v^6;p c n 2;p 2 -2ac", "30:cab;30.3;c,a,b;4;c2v^6;p 2 n a;p -2ac 2", "30:-cba;30.4;-c,b,a;4;c2v^6;p 2 a n;p -2ab 2", "30:bca;30.5;b,c,a;4;c2v^6;p b 2 n;p -2ab -2ab", "30:a-cb;30.6;a,-c,b;4;c2v^6;p n 2 b;p -2bc -2bc", "31;31.1;;4;c2v^7;p m n 21;p 2ac -2", "31:ba-c;31.2;b,a,-c;4;c2v^7;p n m 21;p 2bc -2bc", "31:cab;31.3;c,a,b;4;c2v^7;p 21 m n;p -2ab 2ab", "31:-cba;31.4;-c,b,a;4;c2v^7;p 21 n m;p -2 2ac", "31:bca;31.5;b,c,a;4;c2v^7;p n 21 m;p -2 -2bc", "31:a-cb;31.6;a,-c,b;4;c2v^7;p m 21 n;p -2ab -2", "32;32.1;;4;c2v^8;p b a 2;p 2 -2ab", "32:cab;32.2;c,a,b;4;c2v^8;p 2 c b;p -2bc 2", "32:bca;32.3;b,c,a;4;c2v^8;p c 2 a;p -2ac -2ac", "33;33.1;;4;c2v^9;p n a 21;p 2c -2n", //"33*;33.1;;4;c2v^9;p n a 21*;p 21 -2n", //nonstandard "33:ba-c;33.2;b,a,-c;4;c2v^9;p b n 21;p 2c -2ab", //"33:ba-c*;33.2;b,a,-c;4;c2v^9;p b n 21*;p 21 -2ab", //nonstandard "33:cab;33.3;c,a,b;4;c2v^9;p 21 n b;p -2bc 2a", //"33:cab*;33.3;c,a,b;4;c2v^9;p 21 n b*;p -2bc 21", //nonstandard "33:-cba;33.4;-c,b,a;4;c2v^9;p 21 c n;p -2n 2a", //"33:-cba*;33.4;-c,b,a;4;c2v^9;p 21 c n*;p -2n 21", //nonstandard "33:bca;33.5;b,c,a;4;c2v^9;p c 21 n;p -2n -2ac", "33:a-cb;33.6;a,-c,b;4;c2v^9;p n 21 a;p -2ac -2n", "34;34.1;;4;c2v^10;p n n 2;p 2 -2n", "34:cab;34.2;c,a,b;4;c2v^10;p 2 n n;p -2n 2", "34:bca;34.3;b,c,a;4;c2v^10;p n 2 n;p -2n -2n", "35;35.1;;8;c2v^11;c m m 2;c 2 -2", "35:cab;35.2;c,a,b;8;c2v^11;a 2 m m;a -2 2", "35:bca;35.3;b,c,a;8;c2v^11;b m 2 m;b -2 -2", "36;36.1;;8;c2v^12;c m c 21;c 2c -2", //"36*;36.1;;8;c2v^12;c m c 21*;c 21 -2", //nonstandard "36:ba-c;36.2;b,a,-c;8;c2v^12;c c m 21;c 2c -2c", //"36:ba-c*;36.2;b,a,-c;8;c2v^12;c c m 21*;c 21 -2c", //nonstandard "36:cab;36.3;c,a,b;8;c2v^12;a 21 m a;a -2a 2a", //"36:cab*;36.3;c,a,b;8;c2v^12;a 21 m a*;a -2a 21", //nonstandard "36:-cba;36.4;-c,b,a;8;c2v^12;a 21 a m;a -2 2a", //"36:-cba*;36.4;-c,b,a;8;c2v^12;a 21 a m*;a -2 21", //nonstandard "36:bca;36.5;b,c,a;8;c2v^12;b b 21 m;b -2 -2b", "36:a-cb;36.6;a,-c,b;8;c2v^12;b m 21 b;b -2b -2", "37;37.1;;8;c2v^13;c c c 2;c 2 -2c", "37:cab;37.2;c,a,b;8;c2v^13;a 2 a a;a -2a 2", "37:bca;37.3;b,c,a;8;c2v^13;b b 2 b;b -2b -2b", "38;38.1;;8;c2v^14;a m m 2;a 2 -2", "38:ba-c;38.2;b,a,-c;8;c2v^14;b m m 2;b 2 -2", "38:cab;38.3;c,a,b;8;c2v^14;b 2 m m;b -2 2", "38:-cba;38.4;-c,b,a;8;c2v^14;c 2 m m;c -2 2", "38:bca;38.5;b,c,a;8;c2v^14;c m 2 m;c -2 -2", "38:a-cb;38.6;a,-c,b;8;c2v^14;a m 2 m;a -2 -2", "39;39.1;;8;c2v^15;a e m 2;a 2 -2b", // newer IT name "39;39.1;;8;c2v^15;a b m 2;a 2 -2b", "39:ba-c;39.2;b,a,-c;8;c2v^15;b m e 2;b 2 -2a", "39:ba-c;39.2;b,a,-c;8;c2v^15;b m a 2;b 2 -2a", "39:cab;39.3;c,a,b;8;c2v^15;b 2 e m;b -2a 2", "39:cab;39.3;c,a,b;8;c2v^15;b 2 c m;b -2a 2", "39:-cba;39.4;-c,b,a;8;c2v^15;c 2 m e;c -2a 2", "39:-cba;39.4;-c,b,a;8;c2v^15;c 2 m b;c -2a 2", "39:bca;39.5;b,c,a;8;c2v^15;c m 2 e;c -2a -2a", "39:bca;39.5;b,c,a;8;c2v^15;c m 2 a;c -2a -2a", "39:a-cb;39.6;a,-c,b;8;c2v^15;a e 2 m;a -2b -2b", "39:a-cb;39.6;a,-c,b;8;c2v^15;a c 2 m;a -2b -2b", "40;40.1;;8;c2v^16;a m a 2;a 2 -2a", "40:ba-c;40.2;b,a,-c;8;c2v^16;b b m 2;b 2 -2b", "40:cab;40.3;c,a,b;8;c2v^16;b 2 m b;b -2b 2", "40:-cba;40.4;-c,b,a;8;c2v^16;c 2 c m;c -2c 2", "40:bca;40.5;b,c,a;8;c2v^16;c c 2 m;c -2c -2c", "40:a-cb;40.6;a,-c,b;8;c2v^16;a m 2 a;a -2a -2a", "41;41.1;;8;c2v^17;a e a 2;a 2 -2ab", // newer IT name "41;41.1;;8;c2v^17;a b a 2;a 2 -2ab", "41:ba-c;41.2;b,a,-c;8;c2v^17;b b e 2;b 2 -2ab", "41:ba-c;41.2;b,a,-c;8;c2v^17;b b a 2;b 2 -2ab", "41:cab;41.3;c,a,b;8;c2v^17;b 2 e b;b -2ab 2", "41:cab;41.3;c,a,b;8;c2v^17;b 2 c b;b -2ab 2", "41:-cba;41.4;-c,b,a;8;c2v^17;c 2 c e;c -2ac 2", "41:-cba;41.4;-c,b,a;8;c2v^17;c 2 c b;c -2ac 2", "41:bca;41.5;b,c,a;8;c2v^17;c c 2 e;c -2ac -2ac", "41:bca;41.5;b,c,a;8;c2v^17;c c 2 a;c -2ac -2ac", "41:a-cb;41.6;a,-c,b;8;c2v^17;a e 2 a;a -2ab -2ab", "41:a-cb;41.6;a,-c,b;8;c2v^17;a c 2 a;a -2ab -2ab", "42;42.1;;16;c2v^18;f m m 2;f 2 -2", "42:cab;42.2;c,a,b;16;c2v^18;f 2 m m;f -2 2", "42:bca;42.3;b,c,a;16;c2v^18;f m 2 m;f -2 -2", "43;43.1;;16;c2v^19;f d d 2;f 2 -2d", "43:cab;43.2;c,a,b;16;c2v^19;f 2 d d;f -2d 2", "43:bca;43.3;b,c,a;16;c2v^19;f d 2 d;f -2d -2d", "44;44.1;;8;c2v^20;i m m 2;i 2 -2", "44:cab;44.2;c,a,b;8;c2v^20;i 2 m m;i -2 2", "44:bca;44.3;b,c,a;8;c2v^20;i m 2 m;i -2 -2", "45;45.1;;8;c2v^21;i b a 2;i 2 -2c", "45:cab;45.2;c,a,b;8;c2v^21;i 2 c b;i -2a 2", "45:bca;45.3;b,c,a;8;c2v^21;i c 2 a;i -2b -2b", "46;46.1;;8;c2v^22;i m a 2;i 2 -2a", "46:ba-c;46.2;b,a,-c;8;c2v^22;i b m 2;i 2 -2b", "46:cab;46.3;c,a,b;8;c2v^22;i 2 m b;i -2b 2", "46:-cba;46.4;-c,b,a;8;c2v^22;i 2 c m;i -2c 2", "46:bca;46.5;b,c,a;8;c2v^22;i c 2 m;i -2c -2c", "46:a-cb;46.6;a,-c,b;8;c2v^22;i m 2 a;i -2a -2a", "47;47.1;;8;d2h^1;p m m m;-p 2 2", "48:2;48.1;;8;d2h^2;p n n n :2;-p 2ab 2bc", "48:1;48.2;a,b,c|1/4,1/4,1/4;8;d2h^2;p n n n :1;p 2 2 -1n", "49;49.1;;8;d2h^3;p c c m;-p 2 2c", "49:cab;49.2;c,a,b;8;d2h^3;p m a a;-p 2a 2", "49:bca;49.3;b,c,a;8;d2h^3;p b m b;-p 2b 2b", "50:2;50.1;;8;d2h^4;p b a n :2;-p 2ab 2b", "50:2cab;50.2;c,a,b;8;d2h^4;p n c b :2;-p 2b 2bc", "50:2bca;50.3;b,c,a;8;d2h^4;p c n a :2;-p 2a 2c", "50:1;50.4;a,b,c|1/4,1/4,0;8;d2h^4;p b a n :1;p 2 2 -1ab", "50:1cab;50.5;c,a,b|1/4,1/4,0;8;d2h^4;p n c b :1;p 2 2 -1bc", "50:1bca;50.6;b,c,a|1/4,1/4,0;8;d2h^4;p c n a :1;p 2 2 -1ac", "51;51.1;;8;d2h^5;p m m a;-p 2a 2a", "51:ba-c;51.2;b,a,-c;8;d2h^5;p m m b;-p 2b 2", "51:cab;51.3;c,a,b;8;d2h^5;p b m m;-p 2 2b", "51:-cba;51.4;-c,b,a;8;d2h^5;p c m m;-p 2c 2c", "51:bca;51.5;b,c,a;8;d2h^5;p m c m;-p 2c 2", "51:a-cb;51.6;a,-c,b;8;d2h^5;p m a m;-p 2 2a", "52;52.1;;8;d2h^6;p n n a;-p 2a 2bc", "52:ba-c;52.2;b,a,-c;8;d2h^6;p n n b;-p 2b 2n", "52:cab;52.3;c,a,b;8;d2h^6;p b n n;-p 2n 2b", "52:-cba;52.4;-c,b,a;8;d2h^6;p c n n;-p 2ab 2c", "52:bca;52.5;b,c,a;8;d2h^6;p n c n;-p 2ab 2n", "52:a-cb;52.6;a,-c,b;8;d2h^6;p n a n;-p 2n 2bc", "53;53.1;;8;d2h^7;p m n a;-p 2ac 2", "53:ba-c;53.2;b,a,-c;8;d2h^7;p n m b;-p 2bc 2bc", "53:cab;53.3;c,a,b;8;d2h^7;p b m n;-p 2ab 2ab", "53:-cba;53.4;-c,b,a;8;d2h^7;p c n m;-p 2 2ac", "53:bca;53.5;b,c,a;8;d2h^7;p n c m;-p 2 2bc", "53:a-cb;53.6;a,-c,b;8;d2h^7;p m a n;-p 2ab 2", "54;54.1;;8;d2h^8;p c c a;-p 2a 2ac", "54:ba-c;54.2;b,a,-c;8;d2h^8;p c c b;-p 2b 2c", "54:cab;54.3;c,a,b;8;d2h^8;p b a a;-p 2a 2b", "54:-cba;54.4;-c,b,a;8;d2h^8;p c a a;-p 2ac 2c", "54:bca;54.5;b,c,a;8;d2h^8;p b c b;-p 2bc 2b", "54:a-cb;54.6;a,-c,b;8;d2h^8;p b a b;-p 2b 2ab", "55;55.1;;8;d2h^9;p b a m;-p 2 2ab", "55:cab;55.2;c,a,b;8;d2h^9;p m c b;-p 2bc 2", "55:bca;55.3;b,c,a;8;d2h^9;p c m a;-p 2ac 2ac", "56;56.1;;8;d2h^10;p c c n;-p 2ab 2ac", "56:cab;56.2;c,a,b;8;d2h^10;p n a a;-p 2ac 2bc", "56:bca;56.3;b,c,a;8;d2h^10;p b n b;-p 2bc 2ab", "57;57.1;;8;d2h^11;p b c m;-p 2c 2b", "57:ba-c;57.2;b,a,-c;8;d2h^11;p c a m;-p 2c 2ac", "57:cab;57.3;c,a,b;8;d2h^11;p m c a;-p 2ac 2a", "57:-cba;57.4;-c,b,a;8;d2h^11;p m a b;-p 2b 2a", "57:bca;57.5;b,c,a;8;d2h^11;p b m a;-p 2a 2ab", "57:a-cb;57.6;a,-c,b;8;d2h^11;p c m b;-p 2bc 2c", "58;58.1;;8;d2h^12;p n n m;-p 2 2n", "58:cab;58.2;c,a,b;8;d2h^12;p m n n;-p 2n 2", "58:bca;58.3;b,c,a;8;d2h^12;p n m n;-p 2n 2n", "59:2;59.1;;8;d2h^13;p m m n :2;-p 2ab 2a", "59:2cab;59.2;c,a,b;8;d2h^13;p n m m :2;-p 2c 2bc", "59:2bca;59.3;b,c,a;8;d2h^13;p m n m :2;-p 2c 2a", "59:1;59.4;a,b,c|1/4,1/4,0;8;d2h^13;p m m n :1;p 2 2ab -1ab", "59:1cab;59.5;c,a,b|1/4,1/4,0;8;d2h^13;p n m m :1;p 2bc 2 -1bc", "59:1bca;59.6;b,c,a|1/4,1/4,0;8;d2h^13;p m n m :1;p 2ac 2ac -1ac", "60;60.1;;8;d2h^14;p b c n;-p 2n 2ab", "60:ba-c;60.2;b,a,-c;8;d2h^14;p c a n;-p 2n 2c", "60:cab;60.3;c,a,b;8;d2h^14;p n c a;-p 2a 2n", "60:-cba;60.4;-c,b,a;8;d2h^14;p n a b;-p 2bc 2n", "60:bca;60.5;b,c,a;8;d2h^14;p b n a;-p 2ac 2b", "60:a-cb;60.6;a,-c,b;8;d2h^14;p c n b;-p 2b 2ac", "61;61.1;;8;d2h^15;p b c a;-p 2ac 2ab", "61:ba-c;61.2;b,a,-c;8;d2h^15;p c a b;-p 2bc 2ac", "62;62.1;;8;d2h^16;p n m a;-p 2ac 2n", "62:ba-c;62.2;b,a,-c;8;d2h^16;p m n b;-p 2bc 2a", "62:cab;62.3;c,a,b;8;d2h^16;p b n m;-p 2c 2ab", "62:-cba;62.4;-c,b,a;8;d2h^16;p c m n;-p 2n 2ac", "62:bca;62.5;b,c,a;8;d2h^16;p m c n;-p 2n 2a", "62:a-cb;62.6;a,-c,b;8;d2h^16;p n a m;-p 2c 2n", "63;63.1;;16;d2h^17;c m c m;-c 2c 2", "63:ba-c;63.2;b,a,-c;16;d2h^17;c c m m;-c 2c 2c", "63:cab;63.3;c,a,b;16;d2h^17;a m m a;-a 2a 2a", "63:-cba;63.4;-c,b,a;16;d2h^17;a m a m;-a 2 2a", "63:bca;63.5;b,c,a;16;d2h^17;b b m m;-b 2 2b", "63:a-cb;63.6;a,-c,b;16;d2h^17;b m m b;-b 2b 2", "64;64.1;;16;d2h^18;c m c e;-c 2ac 2", // newer IT name "64;64.1;;16;d2h^18;c m c a;-c 2ac 2", "64:ba-c;64.2;b,a,-c;16;d2h^18;c c m e;-c 2ac 2ac", "64:ba-c;64.2;b,a,-c;16;d2h^18;c c m b;-c 2ac 2ac", "64:cab;64.3;c,a,b;16;d2h^18;a e m a;-a 2ab 2ab", "64:cab;64.3;c,a,b;16;d2h^18;a b m a;-a 2ab 2ab", "64:-cba;64.4;-c,b,a;16;d2h^18;a e a m;-a 2 2ab", "64:-cba;64.4;-c,b,a;16;d2h^18;a c a m;-a 2 2ab", "64:bca;64.5;b,c,a;16;d2h^18;b b e m;-b 2 2ab", "64:bca;64.5;b,c,a;16;d2h^18;b b c m;-b 2 2ab", "64:a-cb;64.6;a,-c,b;16;d2h^18;b m e b;-b 2ab 2", "64:a-cb;64.6;a,-c,b;16;d2h^18;b m a b;-b 2ab 2", "65;65.1;;16;d2h^19;c m m m;-c 2 2", "65:cab;65.2;c,a,b;16;d2h^19;a m m m;-a 2 2", "65:bca;65.3;b,c,a;16;d2h^19;b m m m;-b 2 2", "66;66.1;;16;d2h^20;c c c m;-c 2 2c", "66:cab;66.2;c,a,b;16;d2h^20;a m a a;-a 2a 2", "66:bca;66.3;b,c,a;16;d2h^20;b b m b;-b 2b 2b", "67;67.1;;16;d2h^21;c m m e;-c 2a 2", // newer IT name "67;67.1;;16;d2h^21;c m m a;-c 2a 2", "67:ba-c;67.2;b,a,-c;16;d2h^21;c m m b;-c 2a 2a", "67:cab;67.3;c,a,b;16;d2h^21;a b m m;-a 2b 2b", "67:-cba;67.4;-c,b,a;16;d2h^21;a c m m;-a 2 2b", "67:bca;67.5;b,c,a;16;d2h^21;b m c m;-b 2 2a", "67:a-cb;67.6;a,-c,b;16;d2h^21;b m a m;-b 2a 2", "68:2;68.1;;16;d2h^22;c c c e :2;-c 2a 2ac", "68:2;68.1;;16;d2h^22;c c c a :2;-c 2a 2ac", "68:2ba-c;68.2;b,a,-c;16;d2h^22;c c c b :2;-c 2a 2c", "68:2cab;68.3;c,a,b;16;d2h^22;a b a a :2;-a 2a 2b", "68:2-cba;68.4;-c,b,a;16;d2h^22;a c a a :2;-a 2ab 2b", "68:2bca;68.5;b,c,a;16;d2h^22;b b c b :2;-b 2ab 2b", "68:2a-cb;68.6;a,-c,b;16;d2h^22;b b a b :2;-b 2b 2ab", "68:1;68.7;a,b,c|0,1/4,1/4;16;d2h^22;c c c e :1;c 2 2 -1ac", "68:1;68.7;a,b,c|0,1/4,1/4;16;d2h^22;c c c a :1;c 2 2 -1ac", "68:1ba-c;68.8;b,a,-c|0,1/4,1/4;16;d2h^22;c c c b :1;c 2 2 -1ac", "68:1cab;68.9;c,a,b|0,1/4,1/4;16;d2h^22;a b a a :1;a 2 2 -1ab", "68:1-cba;68.10;-c,b,a|0,1/4,1/4;16;d2h^22;a c a a :1;a 2 2 -1ab", "68:1bca;68.11;b,c,a|0,1/4,1/4;16;d2h^22;b b c b :1;b 2 2 -1ab", "68:1a-cb;68.12;a,-c,b|0,1/4,1/4;16;d2h^22;b b a b :1;b 2 2 -1ab", "69;69.1;;32;d2h^23;f m m m;-f 2 2", "70:2;70.1;;32;d2h^24;f d d d :2;-f 2uv 2vw", "70:1;70.2;a,b,c|-1/8,-1/8,-1/8;32;d2h^24;f d d d :1;f 2 2 -1d", "71;71.1;;16;d2h^25;i m m m;-i 2 2", "72;72.1;;16;d2h^26;i b a m;-i 2 2c", "72:cab;72.2;c,a,b;16;d2h^26;i m c b;-i 2a 2", "72:bca;72.3;b,c,a;16;d2h^26;i c m a;-i 2b 2b", "73;73.1;;16;d2h^27;i b c a;-i 2b 2c", "73:ba-c;73.2;b,a,-c;16;d2h^27;i c a b;-i 2a 2b", "74;74.1;;16;d2h^28;i m m a;-i 2b 2", "74:ba-c;74.2;b,a,-c;16;d2h^28;i m m b;-i 2a 2a", "74:cab;74.3;c,a,b;16;d2h^28;i b m m;-i 2c 2c", "74:-cba;74.4;-c,b,a;16;d2h^28;i c m m;-i 2 2b", "74:bca;74.5;b,c,a;16;d2h^28;i m c m;-i 2 2a", "74:a-cb;74.6;a,-c,b;16;d2h^28;i m a m;-i 2c 2", "75;75.1;;4;c4^1;p 4;p 4", "75:c;75.2;ab;8;c4^1;c 4;c 4", // ITA 75.2 "76;76.1;;4;c4^2;p 41;p 4w", //"76*;76.1;;4;c4^2;p 41*;p 41", //nonstandard "76:c;76.2;ab;8;c4^2;c 41;c 4w", // ITA 76.2 "77;77.1;;4;c4^3;p 42;p 4c", //"77*;77.1;;4;c4^3;p 42*;p 42", //nonstandard "77:c;77.2;ab;8;c4^3;c 42;c 4c", // ITA 77.2 "78;78.1;;4;c4^4;p 43;p 4cw", //"78*;78.1;;4;c4^4;p 43*;p 43", //nonstandard "78:c;78.2;ab;8;c4^4;c 43;c 4cw", // ITA 78.2 "79;79.1;;8;c4^5;i 4;i 4", "79:f;79.2;ab;16;c4^5;f 4;f 4", // ITA 79.2 "80;80.1;;8;c4^6;i 41;i 4bw", "80:f;80.2;ab;16;c4^6;f 41;xyz",//;x,y,z;-x,-y+1/2,z+1/2;-y+3/4,x+1/4,z+1/4;y+1/4,-x+1/4,z+3/4;x,y+1/2,z+1/2;-x,-y,z;-y+1/4,x+1/4,z+3/4;y+3/4,-x+1/4,z+1/4;x+1/2,y+1/2,z;-x+1/2,-y,z+1/2;-y+1/4,x+3/4,z+1/4;y+3/4,-x+3/4,z+3/4;x+1/2,y,z+1/2;-x+1/2,-y+1/2,z;-y+3/4,x+3/4,z+3/4;y+1/4,-x+3/4,z+1/4", // ITA 80.2 "81;81.1;;4;s4^1;p -4;p -4", "81:c;81.2;ab;8;s4^1;c -4;c -4", // ITA 81.2 "82;82.1;;8;s4^2;i -4;i -4", "82:f;82.2;ab;16;s4^2;f -4;f -4", // ITA 82.2 "83;83.1;;8;c4h^1;p 4/m;-p 4", "83:f;83.2;ab;16;c4h^1;c 4/m;-c 4", // ITA 83.2 "84;84.1;;8;c4h^2;p 42/m;-p 4c", //"84*;84.1;;8;c4h^2;p 42/m*;-p 42", //nonstandard "84:c;84.2;ab;16;c4h^2;c 42/m;-c 4c", // ITA 84.2 "85:2;85.1;;8;c4h^3;p 4/n :2;-p 4a", "85:c2;85.2;ab;16;c4h^3;c 4/e :2;xyz",//;x,y,z;-x,-y+1/2,z;-y+1/4,x+1/4,z;y+3/4,-x+1/4,z;-x,-y,-z;x,y+1/2,-z;y+1/4,-x+1/4,-z;-y+3/4,x+1/4,-z;x+1/2,y+1/2,z;-x+1/2,-y,z;-y+3/4,x+3/4,z;y+1/4,-x+3/4,z;-x+1/2,-y+1/2,-z;x+1/2,y,-z;y+3/4,-x+3/4,-z;-y+1/4,x+3/4,-z", // ITA 85.2 "85:1;85.3;a,b,c|-1/4,1/4,0;8;c4h^3;p 4/n :1;p 4ab -1ab", "85:c1;85.4;ab|-1/4,1/4,0;16;c4h^3;c 4/e :1;xyz",//;x,y,z;-x+1/2,-y+1/2,z;-y+1/2,x,z;y,-x+1/2,z;-x+1/2,-y,-z;x,y+1/2,-z;y+1/2,-x+1/2,-z;-y,x,-z;x+1/2,y+1/2,z;-x,-y,z;-y,x+1/2,z;y+1/2,-x,z;-x,-y+1/2,-z;x+1/2,y,-z;y,-x,-z;-y+1/2,x+1/2,-z", // ITA 85.4 "86:2;86.1;;8;c4h^4;p 42/n :2;-p 4bc", "86:1;86.3;a,b,c|-1/4,-1/4,-1/4;8;c4h^4;p 42/n :1;p 4n -1n", "86:c1;86.4;ab|-1/4,-1/4,-1/4;16;c4h^4;c 42/e :1;xyz",//;x,y,z;-x,-y,z;-y,x+1/2,z+1/2;y,-x+1/2,z+1/2;-x,-y+1/2,-z+1/2;x,y+1/2,-z+1/2;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x,z+1/2;y+1/2,-x,z+1/2;-x+1/2,-y,-z+1/2;x+1/2,y,-z+1/2;y,-x,-z;-y,x,-z", // ITA 86.4 "86:c2;86.2;ab;16;c4h^4;c 42/e :2;xyz",//;x,y,z;-x,-y+1/2,z;-y+3/4,x+1/4,z+1/2;y+1/4,-x+1/4,z+1/2;-x,-y,-z;x,y+1/2,-z;y+3/4,-x+1/4,-z+1/2;-y+1/4,x+1/4,-z+1/2;x+1/2,y+1/2,z;-x+1/2,-y,z;-y+1/4,x+3/4,z+1/2;y+3/4,-x+3/4,z+1/2;-x+1/2,-y+1/2,-z;x+1/2,y,-z;y+1/4,-x+3/4,-z+1/2;-y+3/4,x+3/4,-z+1/2", // ITA 86.2 "87;87.1;;16;c4h^5;i 4/m;-i 4", "87:f;87.2;ab;32;c4h^5;f 4/m;xyz",//;x,y,z;-x,-y,z;-y,x,z;y,-x,z;-x,-y,-z;x,y,-z;y,-x,-z;-y,x,-z;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;-y,x+1/2,z+1/2;y,-x+1/2,z+1/2;-x,-y+1/2,-z+1/2;x,y+1/2,-z+1/2;y,-x+1/2,-z+1/2;-y,x+1/2,-z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x+1/2,z;y+1/2,-x+1/2,z;-x+1/2,-y+1/2,-z;x+1/2,y+1/2,-z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;x+1/2,y,z+1/2;-x+1/2,-y,z+1/2;-y+1/2,x,z+1/2;y+1/2,-x,z+1/2;-x+1/2,-y,-z+1/2;x+1/2,y,-z+1/2;y+1/2,-x,-z+1/2;-y+1/2,x,-z+1/2", // ITA 87.2 "88:2;88.1;;16;c4h^6;i 41/a :2;-i 4ad", "88:f2;88.2;ab;32;c4h^6;f 41/d :2;xyz",//;x,y,z;-x+1/4,-y+1/4,z+1/2;-y+1/4,x+1/2,z+1/4;y,-x+3/4,z+3/4;-x,-y,-z;x+1/4,y+1/4,-z+1/2;y+3/4,-x+1/2,-z+3/4;-y,x+1/4,-z+1/4;x,y+1/2,z+1/2;-x+3/4,-y+1/4,z;-y+3/4,x+1/2,z+3/4;y,-x+1/4,z+1/4;-x,-y+1/2,-z+1/2;x+3/4,y+1/4,-z;y+1/4,-x+1/2,-z+1/4;-y,x+3/4,-z+3/4;x+1/2,y+1/2,z;-x+3/4,-y+3/4,z+1/2;-y+3/4,x,z+1/4;y+1/2,-x+5/4,z+3/4;-x+1/2,-y+1/2,-z;x+3/4,y+3/4,-z+1/2;y+1/4,-x,-z+3/4;-y+1/2,x+3/4,-z+1/4;x+1/2,y,z+1/2;-x+1/4,-y+3/4,z;-y+1/4,x,z+3/4;y+1/2,-x+3/4,z+1/4;-x+1/2,-y,-z+1/2;x+1/4,y+3/4,-z;y+3/4,-x,-z+1/4;-y+1/2,x+5/4,-z+3/4", // ITA 88.2 "88:1;88.3;a,b,c|0,-1/4,-1/8;16;c4h^6;i 41/a :1;i 4bw -1bw", "88:f1;88.4;ab|0,-1/4,-1/8;32;c4h^6;f 41/d :1;xyz",//;x,y,z;-x,-y+1/2,z+1/2;-y+1/4,x+3/4,z+1/4;y+3/4,-x+3/4,z+3/4;-x+3/4,-y+1/4,-z+1/4;x+1/4,y+1/4,-z+3/4;y+1/2,-x+1/2,-z;-y,x+1/2,-z+1/2;x,y+1/2,z+1/2;-x+1/2,-y+1/2,z;-y+3/4,x+3/4,z+3/4;y+3/4,-x+1/4,z+1/4;-x+3/4,-y+3/4,-z+3/4;x+3/4,y+1/4,-z+1/4;y,-x+1/2,-z+1/2;-y,x,-z;x+1/2,y+1/2,z;-x+1/2,-y,z+1/2;-y+3/4,x+5/4,z+1/4;y+1/4,-x+5/4,z+3/4;-x+1/4,-y+3/4,-z+1/4;x+3/4,y+3/4,-z+3/4;y,-x,-z;-y+1/2,x,-z+1/2;x+1/2,y,z+1/2;-x,-y,z;-y+1/4,x+5/4,z+3/4;y+1/4,-x+3/4,z+1/4;-x+1/4,-y+5/4,-z+3/4;x+1/4,y+3/4,-z+1/4;y+1/2,-x,-z+1/2;-y+1/2,x+1/2,-z", // ITA 88.4 "89;89.1;;8;d4^1;p 4 2 2;p 4 2", "89:c;89.2;ab;16;d4^1;c 4 2 2;xyz",//;x,y,z;-x,-y,z;-y,x,z;y,-x,z;-y,-x,-z;y,x,-z;-x,y,-z;x,-y,-z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x+1/2,z;y+1/2,-x+1/2,z;-y+1/2,-x+1/2,-z;y+1/2,x+1/2,-z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z", // ITA 89.2 "90;90.1;;8;d4^2;p 4 21 2;p 4ab 2ab", "90:c;90.2;ab;16;d4^2;c 4 2 21;xyz",//;x,y,z;-x,-y,z;-y,x+1/2,z;y,-x+1/2,z;-y,-x+1/2,-z;y,x+1/2,-z;-x,y,-z;x,-y,-z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x,z;y+1/2,-x,z;-y+1/2,-x,-z;y+1/2,x,-z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z", // ITA 90.2 "91;91.1;;8;d4^3;p 41 2 2;p 4w 2c", //"91*;91.1;;8;d4^3;p 41 2 2*;p 41 2c", //nonstandard "91:c;91.2;ab;16;d4^3;c 41 2 2;xyz",//;x,y,z;-x,-y,z+1/2;-y,x,z+1/4;y,-x,z+3/4;-y,-x,-z;y,x,-z+1/2;-x,y,-z+3/4;x,-y,-z+1/4;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z+1/2;-y+1/2,x+1/2,z+1/4;y+1/2,-x+1/2,z+3/4;-y+1/2,-x+1/2,-z;y+1/2,x+1/2,-z+1/2;-x+1/2,y+1/2,-z+3/4;x+1/2,-y+1/2,-z+1/4", // ITA 91.2 "92;92.1;;8;d4^4;p 41 21 2;p 4abw 2nw", "92:c;92.2;ab;16;d4^4;c 41 2 21;xyz",//;x,y,z;-x,-y,z+1/2;-y,x+1/2,z+1/4;y,-x+1/2,z+3/4;-y,-x+1/2,-z+1/4;y,x+1/2,-z+3/4;-x,y,-z;x,-y,-z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z+1/2;-y+1/2,x,z+1/4;y+1/2,-x,z+3/4;-y+1/2,-x,-z+1/4;y+1/2,x,-z+3/4;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z+1/2", // ITA 92.2 "93;93.1;;8;d4^5;p 42 2 2;p 4c 2", //"93*;93.1;;8;d4^5;p 42 2 2*;p 42 2", //nonstandard "93:c;93.2;ab;16;d4^5;c 42 2 2;xyz",//;x,y,z;-x,-y,z;-y,x,z+1/2;y,-x,z+1/2;-y,-x,-z;y,x,-z;-x,y,-z+1/2;x,-y,-z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x+1/2,z+1/2;y+1/2,-x+1/2,z+1/2;-y+1/2,-x+1/2,-z;y+1/2,x+1/2,-z;-x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,-z+1/2", // ITA 93.2 "94;94.1;;8;d4^6;p 42 21 2;p 4n 2n", "94:c;94.2;ab;16;d4^6;c 42 2 21;xyz",//;x,y,z;-x,-y,z;-y,x+1/2,z+1/2;y,-x+1/2,z+1/2;-y,-x+1/2,-z+1/2;y,x+1/2,-z+1/2;-x,y,-z;x,-y,-z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x,z+1/2;y+1/2,-x,z+1/2;-y+1/2,-x,-z+1/2;y+1/2,x,-z+1/2;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z", // ITA 94.2 "95;95.1;;8;d4^7;p 43 2 2;p 4cw 2c", //"95*;95.1;;8;d4^7;p 43 2 2*;p 43 2c", //nonstandard "95:c;95.2;ab;16;d4^7;c 43 2 2;xyz",//;x,y,z;-x,-y,z+1/2;-y,x,z+3/4;y,-x,z+1/4;-y,-x,-z;y,x,-z+1/2;-x,y,-z+1/4;x,-y,-z+3/4;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z+1/2;-y+1/2,x+1/2,z+3/4;y+1/2,-x+1/2,z+1/4;-y+1/2,-x+1/2,-z;y+1/2,x+1/2,-z+1/2;-x+1/2,y+1/2,-z+1/4;x+1/2,-y+1/2,-z+3/4", // ITA 95.2 "96;96.1;;8;d4^8;p 43 21 2;p 4nw 2abw", "96:c;96.2;ab;16;d4^8;c 43 2 21;xyz",//;x,y,z;-x,-y,z+1/2;-y,x+1/2,z+3/4;y,-x+1/2,z+1/4;-y,-x+1/2,-z+3/4;y,x+1/2,-z+1/4;-x,y,-z;x,-y,-z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z+1/2;-y+1/2,x,z+3/4;y+1/2,-x,z+1/4;-y+1/2,-x,-z+3/4;y+1/2,x,-z+1/4;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z+1/2", // ITA 96.2 "97;97.1;;16;d4^9;i 4 2 2;i 4 2", "97:f;97.2;ab;32;d4^9;f 4 2 2;f 4 2", // ITA 97.2 "98;98.1;;16;d4^10;i 41 2 2;i 4bw 2bw", "98:f;98.2;ab;32;d4^10;f 41 2 2;xyz",//;x,y,z;-x,-y+1/2,z+1/2;-y+3/4,x+1/4,z+1/4;y+1/4,-x+1/4,z+3/4;-y+1/4,-x+1/4,-z+3/4;y+3/4,x+1/4,-z+1/4;-x,y+1/2,-z+1/2;x,-y,-z;x,y+1/2,z+1/2;-x,-y,z;-y+1/4,x+1/4,z+3/4;y+3/4,-x+1/4,z+1/4;-y+3/4,-x+1/4,-z+1/4;y+1/4,x+1/4,-z+3/4;-x,y,-z;x,-y+1/2,-z+1/2;x+1/2,y+1/2,z;-x+1/2,-y,z+1/2;-y+1/4,x+3/4,z+1/4;y+3/4,-x+3/4,z+3/4;-y+3/4,-x+3/4,-z+3/4;y+1/4,x+3/4,-z+1/4;-x+1/2,y,-z+1/2;x+1/2,-y+1/2,-z;x+1/2,y,z+1/2;-x+1/2,-y+1/2,z;-y+3/4,x+3/4,z+3/4;y+1/4,-x+3/4,z+1/4;-y+1/4,-x+3/4,-z+1/4;y+3/4,x+3/4,-z+3/4;-x+1/2,y+1/2,-z;x+1/2,-y,-z+1/2", // ITA 98.2 "99;99.1;;8;c4v^1;p 4 m m;p 4 -2", "99:c;99.2;ab;16;c4v^1;c 4 m m;c 4 -2", // ITA 99.2 "100;100.1;;8;c4v^2;p 4 b m;p 4 -2ab", "100:c;100.2;ab;16;c4v^2;c 4 m g1;xyz",//;x,y,z;-x,-y,z;-y,x,z;y,-x,z;y,x+1/2,z;-y,-x+1/2,z;x,-y+1/2,z;-x,y+1/2,z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x+1/2,z;y+1/2,-x+1/2,z;y+1/2,x,z;-y+1/2,-x,z;x+1/2,-y,z;-x+1/2,y,z", // ITA 100.2 "101;101.1;;8;c4v^3;p 42 c m;p 4c -2c", //"101*;101.1;;8;c4v^3;p 42 c m*;p 42 -2c", //nonstandard "101:c;101.2;ab;16;c4v^3;c 42 m c;xyz",//;x,y,z;-x,-y,z;-y,x,z+1/2;y,-x,z+1/2;y,x,z+1/2;-y,-x,z+1/2;x,-y,z;-x,y,z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x+1/2,z+1/2;y+1/2,-x+1/2,z+1/2;y+1/2,x+1/2,z+1/2;-y+1/2,-x+1/2,z+1/2;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z", // ITA 101.2 "102;102.1;;8;c4v^4;p 42 n m;p 4n -2n", "102:c;102.2;ab;16;c4v^4;c 42 m g2;xyz",//;x,y,z;-x,-y,z;-y,x+1/2,z+1/2;y,-x+1/2,z+1/2;y,x+1/2,z+1/2;-y,-x+1/2,z+1/2;x,-y,z;-x,y,z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x,z+1/2;y+1/2,-x,z+1/2;y+1/2,x,z+1/2;-y+1/2,-x,z+1/2;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z", // ITA 102.2 "103;103.1;;8;c4v^5;p 4 c c;p 4 -2c", "103:c;103.2;ab;16;c4v^5;c 4 c c;c 4 -2c", "104;104.1;;8;c4v^6;p 4 n c;p 4 -2n", "104:c;104.2;ab;16;c4v^6;c 4 c g2;xyz",//;x,y,z;-x,-y,z;-y,x,z;y,-x,z;y,x+1/2,z+1/2;-y,-x+1/2,z+1/2;x,-y+1/2,z+1/2;-x,y+1/2,z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x+1/2,z;y+1/2,-x+1/2,z;y+1/2,x,z+1/2;-y+1/2,-x,z+1/2;x+1/2,-y,z+1/2;-x+1/2,y,z+1/2", // ITA 104.2 "105;105.1;;8;c4v^7;p 42 m c;p 4c -2", //"105*;105.1;;8;c4v^7;p 42 m c*;p 42 -2", //nonstandard "105:c;105.2;ab;16;c4v^7;c 42 c m;xyz",//;x,y,z;-x,-y,z;-y,x,z+1/2;y,-x,z+1/2;y,x,z;-y,-x,z;x,-y,z+1/2;-x,y,z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x+1/2,z+1/2;y+1/2,-x+1/2,z+1/2;y+1/2,x+1/2,z;-y+1/2,-x+1/2,z;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2", // ITA 105.2 "106;106.1;;8;c4v^8;p 42 b c;p 4c -2ab", //"106*;106.1;;8;c4v^8;p 42 b c*;p 42 -2ab", //nonstandard "106:c;106.2;ab;16;c4v^8;c 42 c g1;xyz",//;x,y,z;-x,-y,z;-y,x,z+1/2;y,-x,z+1/2;y,x+1/2,z;-y,-x+1/2,z;x,-y+1/2,z+1/2;-x,y+1/2,z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x+1/2,z+1/2;y+1/2,-x+1/2,z+1/2;y+1/2,x,z;-y+1/2,-x,z;x+1/2,-y,z+1/2;-x+1/2,y,z+1/2", // ITA 106.2 "107;107.1;;16;c4v^9;i 4 m m;i 4 -2", "107:f;107.2;ab;32;c4v^9;f 4 m m;f 4 -2", "108;108.1;;16;c4v^10;i 4 c m;i 4 -2c", "108:f;108.2;ab;32;c4v^10;f 4 m c;xyz",//;x,y,z;-x,-y,z;-y,x,z;y,-x,z;y,x,z+1/2;-y,-x,z+1/2;x,-y,z+1/2;-x,y,z+1/2;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;-y,x+1/2,z+1/2;y,-x+1/2,z+1/2;y,x+1/2,z;-y,-x+1/2,z;x,-y+1/2,z;-x,y+1/2,z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x+1/2,z;y+1/2,-x+1/2,z;y+1/2,x+1/2,z+1/2;-y+1/2,-x+1/2,z+1/2;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2;x+1/2,y,z+1/2;-x+1/2,-y,z+1/2;-y+1/2,x,z+1/2;y+1/2,-x,z+1/2;y+1/2,x,z;-y+1/2,-x,z;x+1/2,-y,z;-x+1/2,y,z", // ITA 108.2 "109;109.1;;16;c4v^11;i 41 m d;i 4bw -2", "109:f;109.2;ab;32;c4v^11;f 41 d m;xyz",//;x,y,z;-x,-y+1/2,z+1/2;-y+3/4,x+1/4,z+1/4;y+1/4,-x+1/4,z+3/4;y,x,z;-y,-x+1/2,z+1/2;x+3/4,-y+1/4,z+1/4;-x+1/4,y+1/4,z+3/4;x,y+1/2,z+1/2;-x,-y,z;-y+1/4,x+1/4,z+3/4;y+3/4,-x+1/4,z+1/4;y,x+1/2,z+1/2;-y,-x,z;x+1/4,-y+1/4,z+3/4;-x+3/4,y+1/4,z+1/4;x+1/2,y+1/2,z;-x+1/2,-y,z+1/2;-y+1/4,x+3/4,z+1/4;y+3/4,-x+3/4,z+3/4;y+1/2,x+1/2,z;-y+1/2,-x,z+1/2;x+1/4,-y+3/4,z+1/4;-x+3/4,y+3/4,z+3/4;x+1/2,y,z+1/2;-x+1/2,-y+1/2,z;-y+3/4,x+3/4,z+3/4;y+1/4,-x+3/4,z+1/4;y+1/2,x,z+1/2;-y+1/2,-x+1/2,z;x+3/4,-y+3/4,z+3/4;-x+1/4,y+3/4,z+1/4", // ITA 109.2 "110;110.1;;16;c4v^12;i 41 c d;i 4bw -2c", "110:f;110.2;ab;32;c4v^12;f 41 d c;xyz",//;x,y,z;-x,-y+1/2,z+1/2;-y+3/4,x+1/4,z+1/4;y+1/4,-x+1/4,z+3/4;y,x,z+1/2;-y,-x+1/2,z;x+3/4,-y+1/4,z+3/4;-x+1/4,y+1/4,z+1/4;x,y+1/2,z+1/2;-x,-y,z;-y+1/4,x+1/4,z+3/4;y+3/4,-x+1/4,z+1/4;y,x+1/2,z;-y,-x,z+1/2;x+1/4,-y+1/4,z+1/4;-x+3/4,y+1/4,z+3/4;x+1/2,y+1/2,z;-x+1/2,-y,z+1/2;-y+1/4,x+3/4,z+1/4;y+3/4,-x+3/4,z+3/4;y+1/2,x+1/2,z+1/2;-y+1/2,-x,z;x+1/4,-y+3/4,z+3/4;-x+3/4,y+3/4,z+1/4;x+1/2,y,z+1/2;-x+1/2,-y+1/2,z;-y+3/4,x+3/4,z+3/4;y+1/4,-x+3/4,z+1/4;y+1/2,x,z;-y+1/2,-x+1/2,z+1/2;x+3/4,-y+3/4,z+1/4;-x+1/4,y+3/4,z+3/4", // ITA 110.2 "111;111.1;;8;d2d^1;p -4 2 m;p -4 2", "111:c;111.2;ab;16;d2d^1;c -4 m 2;xyz",//;x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;-y,-x,-z;y,x,-z;x,-y,z;-x,y,z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;-y+1/2,-x+1/2,-z;y+1/2,x+1/2,-z;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z", // ITA 111.2 "112;112.1;;8;d2d^2;p -4 2 c;p -4 2c", "112:c;112.2;ab;16;d2d^2;c -4 c 2;xyz",//;x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;-y,-x,-z+1/2;y,x,-z+1/2;x,-y,z+1/2;-x,y,z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;-y+1/2,-x+1/2,-z+1/2;y+1/2,x+1/2,-z+1/2;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2", // ITA 112.2 "113;113.1;;8;d2d^3;p -4 21 m;p -4 2ab", "113:c;113.2;ab;16;d2d^3;c -4 m 21;xyz",//;x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;-y,-x+1/2,-z;y,x+1/2,-z;x,-y+1/2,z;-x,y+1/2,z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;-y+1/2,-x,-z;y+1/2,x,-z;x+1/2,-y,z;-x+1/2,y,z", // ITA 113.2 "114;114.1;;8;d2d^4;p -4 21 c;p -4 2n", "114:c;114.2;ab;16;d2d^4;c -4 c 21;xyz",//;x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;-y,-x+1/2,-z+1/2;y,x+1/2,-z+1/2;x,-y+1/2,z+1/2;-x,y+1/2,z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;-y+1/2,-x,-z+1/2;y+1/2,x,-z+1/2;x+1/2,-y,z+1/2;-x+1/2,y,z+1/2", // ITA 114.2 "115;115.1;;8;d2d^5;p -4 m 2;p -4 -2", "115:c;115.2;ab;16;d2d^5;c -4 2 m;xyz",//;x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;y,x,z;-y,-x,z;-x,y,-z;x,-y,-z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;y+1/2,x+1/2,z;-y+1/2,-x+1/2,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z", // ITA 115.2 "116;116.1;;8;d2d^6;p -4 c 2;p -4 -2c", "116:c;116.2;ab;16;d2d^6;c -4 2 c;xyz",//;x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;y,x,z+1/2;-y,-x,z+1/2;-x,y,-z+1/2;x,-y,-z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;y+1/2,x+1/2,z+1/2;-y+1/2,-x+1/2,z+1/2;-x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,-z+1/2", // ITA 116.2 "117;117.1;;8;d2d^7;p -4 b 2;p -4 -2ab", "117:c;117.2;ab;16;d2d^7;c -4 2 g1;xyz",//;x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;y,x+1/2,z;-y,-x+1/2,z;-x,y+1/2,-z;x,-y+1/2,-z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;y+1/2,x,z;-y+1/2,-x,z;-x+1/2,y,-z;x+1/2,-y,-z", // ITA 117.2 "118;118.1;;8;d2d^8;p -4 n 2;p -4 -2n", "118:c;118.2;ab;16;d2d^8;c -4 2 g2;xyz",//;x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;y,x+1/2,z+1/2;-y,-x+1/2,z+1/2;-x,y+1/2,-z+1/2;x,-y+1/2,-z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;y+1/2,x,z+1/2;-y+1/2,-x,z+1/2;-x+1/2,y,-z+1/2;x+1/2,-y,-z+1/2", // ITA 118.2 "119;119.1;;16;d2d^9;i -4 m 2;i -4 -2", "119:f;119.2;ab;32;d2d^9;f -4 2 m;xyz",//;x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;y,x,z;-y,-x,z;-x,y,-z;x,-y,-z;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;y,-x+1/2,-z+1/2;-y,x+1/2,-z+1/2;y,x+1/2,z+1/2;-y,-x+1/2,z+1/2;-x,y+1/2,-z+1/2;x,-y+1/2,-z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;y+1/2,x+1/2,z;-y+1/2,-x+1/2,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;x+1/2,y,z+1/2;-x+1/2,-y,z+1/2;y+1/2,-x,-z+1/2;-y+1/2,x,-z+1/2;y+1/2,x,z+1/2;-y+1/2,-x,z+1/2;-x+1/2,y,-z+1/2;x+1/2,-y,-z+1/2", // ITA 119.2 "120;120.1;;16;d2d^10;i -4 c 2;i -4 -2c", "120:f;120.2;ab;32;d2d^10;f -4 2 c;xyz",//;x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;y,x,z+1/2;-y,-x,z+1/2;-x,y,-z+1/2;x,-y,-z+1/2;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;y,-x+1/2,-z+1/2;-y,x+1/2,-z+1/2;y,x+1/2,z;-y,-x+1/2,z;-x,y+1/2,-z;x,-y+1/2,-z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;y+1/2,x+1/2,z+1/2;-y+1/2,-x+1/2,z+1/2;-x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,-z+1/2;x+1/2,y,z+1/2;-x+1/2,-y,z+1/2;y+1/2,-x,-z+1/2;-y+1/2,x,-z+1/2;y+1/2,x,z;-y+1/2,-x,z;-x+1/2,y,-z;x+1/2,-y,-z", // ITA 120.2 "121;121.1;;16;d2d^11;i -4 2 m;i -4 2", "121:f;121.2;ab;32;d2d^11;f -4 m 2;xyz",//;x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;-y,-x,-z;y,x,-z;x,-y,z;-x,y,z;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;y,-x+1/2,-z+1/2;-y,x+1/2,-z+1/2;-y,-x+1/2,-z+1/2;y,x+1/2,-z+1/2;x,-y+1/2,z+1/2;-x,y+1/2,z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;-y+1/2,-x+1/2,-z;y+1/2,x+1/2,-z;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z;x+1/2,y,z+1/2;-x+1/2,-y,z+1/2;y+1/2,-x,-z+1/2;-y+1/2,x,-z+1/2;-y+1/2,-x,-z+1/2;y+1/2,x,-z+1/2;x+1/2,-y,z+1/2;-x+1/2,y,z+1/2", // ITA 121.2 "122;122.1;;16;d2d^12;i -4 2 d;i -4 2bw", "122:f;122.2;ab;32;d2d^12;f -4 d 2;xyz",//;x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;-y+1/4,-x+1/4,-z+3/4;y+1/4,x+1/4,-z+3/4;x+1/4,-y+1/4,z+3/4;-x+1/4,y+1/4,z+3/4;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;y,-x+1/2,-z+1/2;-y,x+1/2,-z+1/2;-y+3/4,-x+1/4,-z+1/4;y+3/4,x+1/4,-z+1/4;x+3/4,-y+1/4,z+1/4;-x+3/4,y+1/4,z+1/4;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;-y+3/4,-x+3/4,-z+3/4;y+3/4,x+3/4,-z+3/4;x+3/4,-y+3/4,z+3/4;-x+3/4,y+3/4,z+3/4;x+1/2,y,z+1/2;-x+1/2,-y,z+1/2;y+1/2,-x,-z+1/2;-y+1/2,x,-z+1/2;-y+1/4,-x+3/4,-z+1/4;y+1/4,x+3/4,-z+1/4;x+1/4,-y+3/4,z+1/4;-x+1/4,y+3/4,z+1/4", // ITA 122.2 "123;123.1;;16;d4h^1;p 4/m m m;-p 4 2", "123:c;123.2;ab;32;d4h^1;c 4/m m m;xyz",//;x,y,z;-x,-y,z;-y,x,z;y,-x,z;-y,-x,-z;y,x,-z;-x,y,-z;x,-y,-z;-x,-y,-z;x,y,-z;y,-x,-z;-y,x,-z;y,x,z;-y,-x,z;x,-y,z;-x,y,z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x+1/2,z;y+1/2,-x+1/2,z;-y+1/2,-x+1/2,-z;y+1/2,x+1/2,-z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;-x+1/2,-y+1/2,-z;x+1/2,y+1/2,-z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;y+1/2,x+1/2,z;-y+1/2,-x+1/2,z;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z", // ITA 123.2 "124;124.1;;16;d4h^2;p 4/m c c;-p 4 2c", "124:c;124.2;ab;32;d4h^2;c 4/m c c;xyz",//;x,y,z;-x,-y,z;-y,x,z;y,-x,z;-y,-x,-z+1/2;y,x,-z+1/2;-x,y,-z+1/2;x,-y,-z+1/2;-x,-y,-z;x,y,-z;y,-x,-z;-y,x,-z;y,x,z+1/2;-y,-x,z+1/2;x,-y,z+1/2;-x,y,z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x+1/2,z;y+1/2,-x+1/2,z;-y+1/2,-x+1/2,-z+1/2;y+1/2,x+1/2,-z+1/2;-x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,-z+1/2;-x+1/2,-y+1/2,-z;x+1/2,y+1/2,-z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;y+1/2,x+1/2,z+1/2;-y+1/2,-x+1/2,z+1/2;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2", // ITA 124.2 "125:2;125.1;;16;d4h^3;p 4/n b m :2;-p 4a 2b", "125:c2;125.2;ab;32;d4h^3;c 4/e m g1 :2;xyz",//;x,y,z;-x,-y+1/2,z;-y+1/4,x+1/4,z;y+3/4,-x+1/4,z;-y+1/4,-x+1/4,-z;y+3/4,x+1/4,-z;-x,y,-z;x,-y+1/2,-z;-x,-y,-z;x,y+1/2,-z;y+1/4,-x+1/4,-z;-y+3/4,x+1/4,-z;y+1/4,x+1/4,z;-y+3/4,-x+1/4,z;x,-y,z;-x,y+1/2,z;x+1/2,y+1/2,z;-x+1/2,-y,z;-y+3/4,x+3/4,z;y+1/4,-x+3/4,z;-y+3/4,-x+3/4,-z;y+1/4,x+3/4,-z;-x+1/2,y+1/2,-z;x+1/2,-y,-z;-x+1/2,-y+1/2,-z;x+1/2,y,-z;y+3/4,-x+3/4,-z;-y+1/4,x+3/4,-z;y+3/4,x+3/4,z;-y+1/4,-x+3/4,z;x+1/2,-y+1/2,z;-x+1/2,y,z", // ITA 125.2 "125:1;125.3;a,b,c|-1/4,-1/4,0;16;d4h^3;p 4/n b m :1;p 4 2 -1ab", "125:c1;125.4;ab|-1/4,-1/4,0;32;d4h^3;c 4/e m g1 :1;xyz",//;x,y,z;-x,-y,z;-y+1/2,x+1/2,z;y+1/2,-x+1/2,z;-y+1/2,-x+1/2,-z;y+1/2,x+1/2,-z;-x,y,-z;x,-y,-z;-x,-y+1/2,-z;x,y+1/2,-z;y,-x+1/2,-z;-y,x+1/2,-z;y,x+1/2,z;-y,-x+1/2,z;x,-y+1/2,z;-x,y+1/2,z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y,x,z;y,-x,z;-y,-x,-z;y,x,-z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;-x+1/2,-y,-z;x+1/2,y,-z;y+1/2,-x,-z;-y+1/2,x,-z;y+1/2,x,z;-y+1/2,-x,z;x+1/2,-y,z;-x+1/2,y,z", // ITA 125.4 "126:2;126.1;;16;d4h^4;p 4/n n c :2;-p 4a 2bc", "126:c1;126.2;ab;32;d4h^4;c 4/e c g2 :2;xyz",//;x,y,z;-x,-y+1/2,z;-y+1/4,x+1/4,z;y+3/4,-x+1/4,z;-y+1/4,-x+1/4,-z+1/2;y+3/4,x+1/4,-z+1/2;-x,y,-z+1/2;x,-y+1/2,-z+1/2;-x,-y,-z;x,y+1/2,-z;y+1/4,-x+1/4,-z;-y+3/4,x+1/4,-z;y+1/4,x+1/4,z+1/2;-y+3/4,-x+1/4,z+1/2;x,-y,z+1/2;-x,y+1/2,z+1/2;x+1/2,y+1/2,z;-x+1/2,-y,z;-y+3/4,x+3/4,z;y+1/4,-x+3/4,z;-y+3/4,-x+3/4,-z+1/2;y+1/4,x+3/4,-z+1/2;-x+1/2,y+1/2,-z+1/2;x+1/2,-y,-z+1/2;-x+1/2,-y+1/2,-z;x+1/2,y,-z;y+3/4,-x+3/4,-z;-y+1/4,x+3/4,-z;y+3/4,x+3/4,z+1/2;-y+1/4,-x+3/4,z+1/2;x+1/2,-y+1/2,z+1/2;-x+1/2,y,z+1/2", // ITA 126.2 "126:1;126.3;a,b,c|-1/4,-1/4,-1/4;16;d4h^4;p 4/n n c :1;p 4 2 -1n", "126:c4;126.4;ab|-1/4,-1/4,-1/4;32;d4h^4;c 4/e c g2 :1;xyz",//;x,y,z;-x,-y,z;-y+1/2,x+1/2,z;y+1/2,-x+1/2,z;-y+1/2,-x+1/2,-z;y+1/2,x+1/2,-z;-x,y,-z;x,-y,-z;-x,-y+1/2,-z+1/2;x,y+1/2,-z+1/2;y,-x+1/2,-z+1/2;-y,x+1/2,-z+1/2;y,x+1/2,z+1/2;-y,-x+1/2,z+1/2;x,-y+1/2,z+1/2;-x,y+1/2,z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y,x,z;y,-x,z;-y,-x,-z;y,x,-z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;-x+1/2,-y,-z+1/2;x+1/2,y,-z+1/2;y+1/2,-x,-z+1/2;-y+1/2,x,-z+1/2;y+1/2,x,z+1/2;-y+1/2,-x,z+1/2;x+1/2,-y,z+1/2;-x+1/2,y,z+1/2", // ITA 126.4 "127;127.1;;16;d4h^5;p 4/m b m;-p 4 2ab", "127:c;127.2;ab;32;d4h^5;c 4/m m g1;xyz",//;x,y,z;-x,-y,z;-y,x,z;y,-x,z;-y,-x+1/2,-z;y,x+1/2,-z;-x,y+1/2,-z;x,-y+1/2,-z;-x,-y,-z;x,y,-z;y,-x,-z;-y,x,-z;y,x+1/2,z;-y,-x+1/2,z;x,-y+1/2,z;-x,y+1/2,z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x+1/2,z;y+1/2,-x+1/2,z;-y+1/2,-x,-z;y+1/2,x,-z;-x+1/2,y,-z;x+1/2,-y,-z;-x+1/2,-y+1/2,-z;x+1/2,y+1/2,-z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;y+1/2,x,z;-y+1/2,-x,z;x+1/2,-y,z;-x+1/2,y,z", // ITA 127.2 "128;128.1;;16;d4h^6;p 4/m n c;-p 4 2n", "128:c;128.2;ab;32;d4h^6;c 4/m c g2;xyz",//;x,y,z;-x,-y,z;-y,x,z;y,-x,z;y+1/2,x,-z+1/2;-y+1/2,-x,-z+1/2;x+1/2,-y,-z+1/2;-x+1/2,y,-z+1/2;-x,-y,-z;x,y,-z;y,-x,-z;-y,x,-z;-y+1/2,-x,z+1/2;y+1/2,x,z+1/2;-x+1/2,y,z+1/2;x+1/2,-y,z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x+1/2,z;y+1/2,-x+1/2,z;y,x+1/2,-z+1/2;-y,-x+1/2,-z+1/2;x,-y+1/2,-z+1/2;-x,y+1/2,-z+1/2;-x+1/2,-y+1/2,-z;x+1/2,y+1/2,-z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;-y,-x+1/2,z+1/2;y,x+1/2,z+1/2;-x,y+1/2,z+1/2;x,-y+1/2,z+1/2", // ITA 128.2 "129:2;129.1;;16;d4h^7;p 4/n m m :2;-p 4a 2a", "129:c2;129.2;ab;32;d4h^7;c 4/e m m :2;xyz",//;x,y,z;-x,-y+1/2,z;-y+1/4,x+1/4,z;y+3/4,-x+1/4,z;-y+3/4,-x+1/4,-z;y+1/4,x+1/4,-z;-x,y+1/2,-z;x,-y,-z;-x,-y,-z;x,y+1/2,-z;y+1/4,-x+1/4,-z;-y+3/4,x+1/4,-z;y+3/4,x+1/4,z;-y+1/4,-x+1/4,z;x,-y+1/2,z;-x,y,z;x+1/2,y+1/2,z;-x+1/2,-y,z;-y+3/4,x+3/4,z;y+1/4,-x+3/4,z;-y+1/4,-x+3/4,-z;y+3/4,x+3/4,-z;-x+1/2,y,-z;x+1/2,-y+1/2,-z;-x+1/2,-y+1/2,-z;x+1/2,y,-z;y+3/4,-x+3/4,-z;-y+1/4,x+3/4,-z;y+1/4,x+3/4,z;-y+3/4,-x+3/4,z;x+1/2,-y,z;-x+1/2,y+1/2,z", // ITA 129.2 "129:1;129.3;a,b,c|-1/4,1/4,0;16;d4h^7;p 4/n m m :1;p 4ab 2ab -1ab", "129:c1;129.4;ab|-1/4,1/4,0;32;d4h^7;c 4/e m m :1;xyz",//;x,y,z;-x+1/2,-y+1/2,z;-y+1/2,x,z;y,-x+1/2,z;-y,-x+1/2,-z;y+1/2,x,-z;-x+1/2,y+1/2,-z;x,-y,-z;-x+1/2,-y,-z;x,y+1/2,-z;y+1/2,-x+1/2,-z;-y,x,-z;y,x,z;-y+1/2,-x+1/2,z;x,-y+1/2,z;-x+1/2,y,z;x+1/2,y+1/2,z;-x,-y,z;-y,x+1/2,z;y+1/2,-x,z;-y+1/2,-x,-z;y,x+1/2,-z;-x,y,-z;x+1/2,-y+1/2,-z;-x,-y+1/2,-z;x+1/2,y,-z;y,-x,-z;-y+1/2,x+1/2,-z;y+1/2,x+1/2,z;-y,-x,z;x+1/2,-y,z;-x,y+1/2,z", // ITA 129.4 "130:2;130.1;;16;d4h^8;p 4/n c c :2;-p 4a 2ac", "130:c2;130.2;ab;32;d4h^8;c 4/e c c :2;xyz",//;x,y,z;-x,-y+1/2,z;-y+1/4,x+1/4,z;y+3/4,-x+1/4,z;-y+3/4,-x+1/4,-z+1/2;y+1/4,x+1/4,-z+1/2;-x,y+1/2,-z+1/2;x,-y,-z+1/2;-x,-y,-z;x,y+1/2,-z;y+1/4,-x+1/4,-z;-y+3/4,x+1/4,-z;y+3/4,x+1/4,z+1/2;-y+1/4,-x+1/4,z+1/2;x,-y+1/2,z+1/2;-x,y,z+1/2;x+1/2,y+1/2,z;-x+1/2,-y,z;-y+3/4,x+3/4,z;y+1/4,-x+3/4,z;-y+1/4,-x+3/4,-z+1/2;y+3/4,x+3/4,-z+1/2;-x+1/2,y,-z+1/2;x+1/2,-y+1/2,-z+1/2;-x+1/2,-y+1/2,-z;x+1/2,y,-z;y+3/4,-x+3/4,-z;-y+1/4,x+3/4,-z;y+1/4,x+3/4,z+1/2;-y+3/4,-x+3/4,z+1/2;x+1/2,-y,z+1/2;-x+1/2,y+1/2,z+1/2", // ITA 130.2 "130:1;130.3;a,b,c|-1/4,1/4,0;16;d4h^8;p 4/n c c :1;p 4ab 2n -1ab", "130:c1;130.4;ab|-1/4,1/4,0;32;d4h^8;c 4/e c c :1;xyz",//;x,y,z;-x+1/2,-y+1/2,z;-y+1/2,x,z;y,-x+1/2,z;-y,-x+1/2,-z+1/2;y+1/2,x,-z+1/2;-x+1/2,y+1/2,-z+1/2;x,-y,-z+1/2;-x+1/2,-y,-z;x,y+1/2,-z;y+1/2,-x+1/2,-z;-y,x,-z;y,x,z+1/2;-y+1/2,-x+1/2,z+1/2;x,-y+1/2,z+1/2;-x+1/2,y,z+1/2;x+1/2,y+1/2,z;-x,-y,z;-y,x+1/2,z;y+1/2,-x,z;-y+1/2,-x,-z+1/2;y,x+1/2,-z+1/2;-x,y,-z+1/2;x+1/2,-y+1/2,-z+1/2;-x,-y+1/2,-z;x+1/2,y,-z;y,-x,-z;-y+1/2,x+1/2,-z;y+1/2,x+1/2,z+1/2;-y,-x,z+1/2;x+1/2,-y,z+1/2;-x,y+1/2,z+1/2", // ITA 130.4 "131;131.1;;16;d4h^9;p 42/m m c;-p 4c 2", "131:c;131.2;ab;32;d4h^9;c 42/m c m;xyz",//;x,y,z;-x,-y,z;-y,x,z+1/2;y,-x,z+1/2;-y,-x,-z;y,x,-z;-x,y,-z+1/2;x,-y,-z+1/2;-x,-y,-z;x,y,-z;y,-x,-z+1/2;-y,x,-z+1/2;y,x,z;-y,-x,z;x,-y,z+1/2;-x,y,z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x+1/2,z+1/2;y+1/2,-x+1/2,z+1/2;-y+1/2,-x+1/2,-z;y+1/2,x+1/2,-z;-x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,-z+1/2;-x+1/2,-y+1/2,-z;x+1/2,y+1/2,-z;y+1/2,-x+1/2,-z+1/2;-y+1/2,x+1/2,-z+1/2;y+1/2,x+1/2,z;-y+1/2,-x+1/2,z;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2", // ITA 131.2 "132;132.1;;16;d4h^10;p 42/m c m;-p 4c 2c", "132:c;132.2;ab;32;d4h^10;c 42/m m c;xyz",//;x,y,z;-x,-y,z;-y,x,z+1/2;y,-x,z+1/2;-y,-x,-z+1/2;y,x,-z+1/2;-x,y,-z;x,-y,-z;-x,-y,-z;x,y,-z;y,-x,-z+1/2;-y,x,-z+1/2;y,x,z+1/2;-y,-x,z+1/2;x,-y,z;-x,y,z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x+1/2,z+1/2;y+1/2,-x+1/2,z+1/2;-y+1/2,-x+1/2,-z+1/2;y+1/2,x+1/2,-z+1/2;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;-x+1/2,-y+1/2,-z;x+1/2,y+1/2,-z;y+1/2,-x+1/2,-z+1/2;-y+1/2,x+1/2,-z+1/2;y+1/2,x+1/2,z+1/2;-y+1/2,-x+1/2,z+1/2;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z", // ITA 132.2 "133:2;133.1;;16;d4h^11;p 42/n b c :2;-p 4ac 2b", "133:c1;133.2;ab;32;d4h^11;c 42/e c g1 :2;xyz",//;x,y,z;-x,-y+1/2,z;-y+1/4,x+1/4,z+1/2;y+3/4,-x+1/4,z+1/2;-y+1/4,-x+1/4,-z;y+3/4,x+1/4,-z;-x,y,-z+1/2;x,-y+1/2,-z+1/2;-x,-y,-z;x,y+1/2,-z;y+1/4,-x+1/4,-z+1/2;-y+3/4,x+1/4,-z+1/2;y+1/4,x+1/4,z;-y+3/4,-x+1/4,z;x,-y,z+1/2;-x,y+1/2,z+1/2;x+1/2,y+1/2,z;-x+1/2,-y,z;-y+3/4,x+3/4,z+1/2;y+1/4,-x+3/4,z+1/2;-y+3/4,-x+3/4,-z;y+1/4,x+3/4,-z;-x+1/2,y+1/2,-z+1/2;x+1/2,-y,-z+1/2;-x+1/2,-y+1/2,-z;x+1/2,y,-z;y+3/4,-x+3/4,-z+1/2;-y+1/4,x+3/4,-z+1/2;y+3/4,x+3/4,z;-y+1/4,-x+3/4,z;x+1/2,-y+1/2,z+1/2;-x+1/2,y,z+1/2", // ITA 133.2 "133:1;133.3;a,b,c|-1/4,1/4,-1/4;16;d4h^11;p 42/n b c :1;p 4n 2c -1n", "133:c2;133.4;ab|-1/4,1/4,-1/4;32;d4h^11;c 42/e c g1 :1;xyz",//;x,y,z;-x+1/2,-y+1/2,z;-y+1/2,x,z+1/2;y,-x+1/2,z+1/2;-y+1/2,-x+1/2,-z+1/2;y,x,-z+1/2;-x+1/2,y,-z;x,-y+1/2,-z;-x+1/2,-y,-z+1/2;x,y+1/2,-z+1/2;y+1/2,-x+1/2,-z;-y,x,-z;y+1/2,x,z;-y,-x+1/2,z;x,-y,z+1/2;-x+1/2,y+1/2,z+1/2;x+1/2,y+1/2,z;-x,-y,z;-y,x+1/2,z+1/2;y+1/2,-x,z+1/2;-y,-x,-z+1/2;y+1/2,x+1/2,-z+1/2;-x,y+1/2,-z;x+1/2,-y,-z;-x,-y+1/2,-z+1/2;x+1/2,y,-z+1/2;y,-x,-z;-y+1/2,x+1/2,-z;y,x+1/2,z;-y+1/2,-x,z;x+1/2,-y+1/2,z+1/2;-x,y,z+1/2", // ITA 133.4 "134:2;134.1;;16;d4h^12;p 42/n n m :2;-p 4ac 2bc", "134:c2;134.2;ab;32;d4h^12;c 42/e m g2 :2;xyz",//;x,y,z;-x,-y+1/2,z;-y+1/4,x+1/4,z+1/2;y+3/4,-x+1/4,z+1/2;-y+1/4,-x+1/4,-z+1/2;y+3/4,x+1/4,-z+1/2;-x,y,-z;x,-y+1/2,-z;-x,-y,-z;x,y+1/2,-z;y+1/4,-x+1/4,-z+1/2;-y+3/4,x+1/4,-z+1/2;y+1/4,x+1/4,z+1/2;-y+3/4,-x+1/4,z+1/2;x,-y,z;-x,y+1/2,z;x+1/2,y+1/2,z;-x+1/2,-y,z;-y+3/4,x+3/4,z+1/2;y+1/4,-x+3/4,z+1/2;-y+3/4,-x+3/4,-z+1/2;y+1/4,x+3/4,-z+1/2;-x+1/2,y+1/2,-z;x+1/2,-y,-z;-x+1/2,-y+1/2,-z;x+1/2,y,-z;y+3/4,-x+3/4,-z+1/2;-y+1/4,x+3/4,-z+1/2;y+3/4,x+3/4,z+1/2;-y+1/4,-x+3/4,z+1/2;x+1/2,-y+1/2,z;-x+1/2,y,z", // ITA 134.2 "134:1;134.3;a,b,c|-1/4,1/4,-1/4;16;d4h^12;p 42/n n m :1;p 4n 2 -1n", "134:c1;134.4;ab|-1/4,1/4,-1/4;32;d4h^12;c 42/e m g2 :1;xyz",//;x,y,z;-x+1/2,-y+1/2,z;-y+1/2,x,z+1/2;y,-x+1/2,z+1/2;-y+1/2,-x+1/2,-z;y,x,-z;-x+1/2,y,-z+1/2;x,-y+1/2,-z+1/2;-x+1/2,-y,-z+1/2;x,y+1/2,-z+1/2;y+1/2,-x+1/2,-z;-y,x,-z;y+1/2,x,z+1/2;-y,-x+1/2,z+1/2;x,-y,z;-x+1/2,y+1/2,z;x+1/2,y+1/2,z;-x,-y,z;-y,x+1/2,z+1/2;y+1/2,-x,z+1/2;-y,-x,-z;y+1/2,x+1/2,-z;-x,y+1/2,-z+1/2;x+1/2,-y,-z+1/2;-x,-y+1/2,-z+1/2;x+1/2,y,-z+1/2;y,-x,-z;-y+1/2,x+1/2,-z;y,x+1/2,z+1/2;-y+1/2,-x,z+1/2;x+1/2,-y+1/2,z;-x,y,z", // ITA 134.4 "135;135.1;;16;d4h^13;p 42/m b c;-p 4c 2ab", //"135*;135.1;;16;d4h^13;p 42/m b c*;-p 42 2ab", //nonstandard "135:c;135.2;ab;32;d4h^13;c 42/m c g1;xyz",//;x,y,z;-x,-y,z;-y,x,z+1/2;y,-x,z+1/2;-y,-x+1/2,-z;y,x+1/2,-z;-x,y+1/2,-z+1/2;x,-y+1/2,-z+1/2;-x,-y,-z;x,y,-z;y,-x,-z+1/2;-y,x,-z+1/2;y,x+1/2,z;-y,-x+1/2,z;x,-y+1/2,z+1/2;-x,y+1/2,z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x+1/2,z+1/2;y+1/2,-x+1/2,z+1/2;-y+1/2,-x,-z;y+1/2,x,-z;-x+1/2,y,-z+1/2;x+1/2,-y,-z+1/2;-x+1/2,-y+1/2,-z;x+1/2,y+1/2,-z;y+1/2,-x+1/2,-z+1/2;-y+1/2,x+1/2,-z+1/2;y+1/2,x,z;-y+1/2,-x,z;x+1/2,-y,z+1/2;-x+1/2,y,z+1/2", // ITA 135.2 "136;136.1;;16;d4h^14;p 42/m n m;-p 4n 2n", "136:c;136.2;ab;32;d4h^14;c 42/m m g2;xyz",//;x,y,z;-x,-y,z;-y,x+1/2,z+1/2;y,-x+1/2,z+1/2;-y,-x+1/2,-z+1/2;y,x+1/2,-z+1/2;-x,y,-z;x,-y,-z;-x,-y,-z;x,y,-z;y,-x+1/2,-z+1/2;-y,x+1/2,-z+1/2;y,x+1/2,z+1/2;-y,-x+1/2,z+1/2;x,-y,z;-x,y,z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x,z+1/2;y+1/2,-x,z+1/2;-y+1/2,-x,-z+1/2;y+1/2,x,-z+1/2;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;-x+1/2,-y+1/2,-z;x+1/2,y+1/2,-z;y+1/2,-x,-z+1/2;-y+1/2,x,-z+1/2;y+1/2,x,z+1/2;-y+1/2,-x,z+1/2;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z", // ITA 136.2 "137:2;137.1;;16;d4h^15;p 42/n m c :2;-p 4ac 2a", "137:c1;137.2;ab;32;d4h^15;c 42/e c m :2;xyz",//;x,y,z;-x,-y+1/2,z;-y+1/4,x+1/4,z+1/2;y+3/4,-x+1/4,z+1/2;-y+3/4,-x+1/4,-z;y+1/4,x+1/4,-z;-x,y+1/2,-z+1/2;x,-y,-z+1/2;-x,-y,-z;x,y+1/2,-z;y+1/4,-x+1/4,-z+1/2;-y+3/4,x+1/4,-z+1/2;y+3/4,x+1/4,z;-y+1/4,-x+1/4,z;x,-y+1/2,z+1/2;-x,y,z+1/2;x+1/2,y+1/2,z;-x+1/2,-y,z;-y+3/4,x+3/4,z+1/2;y+1/4,-x+3/4,z+1/2;-y+1/4,-x+3/4,-z;y+3/4,x+3/4,-z;-x+1/2,y,-z+1/2;x+1/2,-y+1/2,-z+1/2;-x+1/2,-y+1/2,-z;x+1/2,y,-z;y+3/4,-x+3/4,-z+1/2;-y+1/4,x+3/4,-z+1/2;y+1/4,x+3/4,z;-y+3/4,-x+3/4,z;x+1/2,-y,z+1/2;-x+1/2,y+1/2,z+1/2", // ITA 137.2 "137:1;137.3;a,b,c|-1/4,1/4,-1/4;16;d4h^15;p 42/n m c :1;p 4n 2n -1n", "137:c2;137.4;ab|-1/4,1/4,-1/4;32;d4h^15;c 42/e c m :1;xyz",//;x,y,z;-x+1/2,-y+1/2,z;-y+1/2,x,z+1/2;y,-x+1/2,z+1/2;-y,-x+1/2,-z+1/2;y+1/2,x,-z+1/2;-x+1/2,y+1/2,-z;x,-y,-z;-x+1/2,-y,-z+1/2;x,y+1/2,-z+1/2;y+1/2,-x+1/2,-z;-y,x,-z;y,x,z;-y+1/2,-x+1/2,z;x,-y+1/2,z+1/2;-x+1/2,y,z+1/2;x+1/2,y+1/2,z;-x,-y,z;-y,x+1/2,z+1/2;y+1/2,-x,z+1/2;-y+1/2,-x,-z+1/2;y,x+1/2,-z+1/2;-x,y,-z;x+1/2,-y+1/2,-z;-x,-y+1/2,-z+1/2;x+1/2,y,-z+1/2;y,-x,-z;-y+1/2,x+1/2,-z;y+1/2,x+1/2,z;-y,-x,z;x+1/2,-y,z+1/2;-x,y+1/2,z+1/2", // ITA 137.4 "138:2;138.1;;16;d4h^16;p 42/n c m :2;-p 4ac 2ac", "138:c2;138.2;ab;32;d4h^16;c 42/e m c :2;xyz",//;x,y,z;-x,-y+1/2,z;-y+1/4,x+1/4,z+1/2;y+3/4,-x+1/4,z+1/2;-y+3/4,-x+1/4,-z+1/2;y+1/4,x+1/4,-z+1/2;-x,y+1/2,-z;x,-y,-z;-x,-y,-z;x,y+1/2,-z;y+1/4,-x+1/4,-z+1/2;-y+3/4,x+1/4,-z+1/2;y+3/4,x+1/4,z+1/2;-y+1/4,-x+1/4,z+1/2;x,-y+1/2,z;-x,y,z;x+1/2,y+1/2,z;-x+1/2,-y,z;-y+3/4,x+3/4,z+1/2;y+1/4,-x+3/4,z+1/2;-y+1/4,-x+3/4,-z+1/2;y+3/4,x+3/4,-z+1/2;-x+1/2,y,-z;x+1/2,-y+1/2,-z;-x+1/2,-y+1/2,-z;x+1/2,y,-z;y+3/4,-x+3/4,-z+1/2;-y+1/4,x+3/4,-z+1/2;y+1/4,x+3/4,z+1/2;-y+3/4,-x+3/4,z+1/2;x+1/2,-y,z;-x+1/2,y+1/2,z", // ITA 138.2 "138:1;138.3;a,b,c|-1/4,1/4,-1/4;16;d4h^16;p 42/n c m :1;p 4n 2ab -1n", "138:c1;138.4;ab|-1/4,1/4,-1/4;32;d4h^16;c 42/e m c :1;xyz",//;x,y,z;-x+1/2,-y+1/2,z;-y+1/2,x,z+1/2;y,-x+1/2,z+1/2;-y,-x+1/2,-z;y+1/2,x,-z;-x+1/2,y+1/2,-z+1/2;x,-y,-z+1/2;-x+1/2,-y,-z+1/2;x,y+1/2,-z+1/2;y+1/2,-x+1/2,-z;-y,x,-z;y,x,z+1/2;-y+1/2,-x+1/2,z+1/2;x,-y+1/2,z;-x+1/2,y,z;x+1/2,y+1/2,z;-x,-y,z;-y,x+1/2,z+1/2;y+1/2,-x,z+1/2;-y+1/2,-x,-z;y,x+1/2,-z;-x,y,-z+1/2;x+1/2,-y+1/2,-z+1/2;-x,-y+1/2,-z+1/2;x+1/2,y,-z+1/2;y,-x,-z;-y+1/2,x+1/2,-z;y+1/2,x+1/2,z+1/2;-y,-x,z+1/2;x+1/2,-y,z;-x,y+1/2,z", // ITA 138.4 "139;139.1;;32;d4h^17;i 4/m m m;-i 4 2", "139:f;139.2;ab;64;d4h^17;f 4/m m m;xyz",//;x,y,z;-x,-y,z;-y,x,z;y,-x,z;-y,-x,-z;y,x,-z;-x,y,-z;x,-y,-z;-x,-y,-z;x,y,-z;y,-x,-z;-y,x,-z;y,x,z;-y,-x,z;x,-y,z;-x,y,z;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;-y,x+1/2,z+1/2;y,-x+1/2,z+1/2;-y,-x+1/2,-z+1/2;y,x+1/2,-z+1/2;-x,y+1/2,-z+1/2;x,-y+1/2,-z+1/2;-x,-y+1/2,-z+1/2;x,y+1/2,-z+1/2;y,-x+1/2,-z+1/2;-y,x+1/2,-z+1/2;y,x+1/2,z+1/2;-y,-x+1/2,z+1/2;x,-y+1/2,z+1/2;-x,y+1/2,z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x+1/2,z;y+1/2,-x+1/2,z;-y+1/2,-x+1/2,-z;y+1/2,x+1/2,-z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;-x+1/2,-y+1/2,-z;x+1/2,y+1/2,-z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;y+1/2,x+1/2,z;-y+1/2,-x+1/2,z;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z;x+1/2,y,z+1/2;-x+1/2,-y,z+1/2;-y+1/2,x,z+1/2;y+1/2,-x,z+1/2;-y+1/2,-x,-z+1/2;y+1/2,x,-z+1/2;-x+1/2,y,-z+1/2;x+1/2,-y,-z+1/2;-x+1/2,-y,-z+1/2;x+1/2,y,-z+1/2;y+1/2,-x,-z+1/2;-y+1/2,x,-z+1/2;y+1/2,x,z+1/2;-y+1/2,-x,z+1/2;x+1/2,-y,z+1/2;-x+1/2,y,z+1/2", // ITA 139.2 "140;140.1;;32;d4h^18;i 4/m c m;-i 4 2c", "140:f;140.2;ab;64;d4h^18;f 4/m m c;xyz",//;x,y,z;-x,-y,z;-y,x,z;y,-x,z;-y,-x,-z+1/2;y,x,-z+1/2;-x,y,-z+1/2;x,-y,-z+1/2;-x,-y,-z;x,y,-z;y,-x,-z;-y,x,-z;y,x,z+1/2;-y,-x,z+1/2;x,-y,z+1/2;-x,y,z+1/2;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;-y,x+1/2,z+1/2;y,-x+1/2,z+1/2;-y,-x+1/2,-z;y,x+1/2,-z;-x,y+1/2,-z;x,-y+1/2,-z;-x,-y+1/2,-z+1/2;x,y+1/2,-z+1/2;y,-x+1/2,-z+1/2;-y,x+1/2,-z+1/2;y,x+1/2,z;-y,-x+1/2,z;x,-y+1/2,z;-x,y+1/2,z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-y+1/2,x+1/2,z;y+1/2,-x+1/2,z;-y+1/2,-x+1/2,-z+1/2;y+1/2,x+1/2,-z+1/2;-x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,-z+1/2;-x+1/2,-y+1/2,-z;x+1/2,y+1/2,-z;y+1/2,-x+1/2,-z;-y+1/2,x+1/2,-z;y+1/2,x+1/2,z+1/2;-y+1/2,-x+1/2,z+1/2;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2;x+1/2,y,z+1/2;-x+1/2,-y,z+1/2;-y+1/2,x,z+1/2;y+1/2,-x,z+1/2;-y+1/2,-x,-z;y+1/2,x,-z;-x+1/2,y,-z;x+1/2,-y,-z;-x+1/2,-y,-z+1/2;x+1/2,y,-z+1/2;y+1/2,-x,-z+1/2;-y+1/2,x,-z+1/2;y+1/2,x,z;-y+1/2,-x,z;x+1/2,-y,z;-x+1/2,y,z", // ITA 140.2 "141:2;141.1;;32;d4h^19;i 41/a m d :2;-i 4bd 2", "141:f2;141.2;ab;64;d4h^19;f 41/d d m :2;xyz",//;x,y,z;-x+1/4,-y+1/4,z+1/2;-y+3/4,x+1/2,z+1/4;y,-x+1/4,z+3/4;-y+1/4,-x+1/4,-z+1/2;y,x,-z;-x+3/4,y+1/2,-z+1/4;x,-y+1/4,-z+3/4;-x,-y,-z;x+1/4,y+1/4,-z+1/2;y+1/4,-x+1/2,-z+3/4;-y,x+3/4,-z+1/4;y+1/4,x+1/4,z+1/2;-y,-x,z;x+1/4,-y+1/2,z+3/4;-x,y+3/4,z+1/4;x,y+1/2,z+1/2;-x+3/4,-y+1/4,z;-y+1/4,x+1/2,z+3/4;y,-x+3/4,z+1/4;-y+3/4,-x+1/4,-z;y,x+1/2,-z+1/2;-x+1/4,y+1/2,-z+3/4;x,-y+3/4,-z+1/4;-x,-y+1/2,-z+1/2;x+3/4,y+1/4,-z;y+3/4,-x+1/2,-z+1/4;-y,x+1/4,-z+3/4;y+3/4,x+1/4,z;-y,-x+1/2,z+1/2;x+3/4,-y+1/2,z+1/4;-x,y+1/4,z+3/4;x+1/2,y+1/2,z;-x+3/4,-y+3/4,z+1/2;-y+1/4,x,z+1/4;y+1/2,-x+3/4,z+3/4;-y+3/4,-x+3/4,-z+1/2;y+1/2,x+1/2,-z;-x+1/4,y,-z+1/4;x+1/2,-y+3/4,-z+3/4;-x+1/2,-y+1/2,-z;x+3/4,y+3/4,-z+1/2;y+3/4,-x,-z+3/4;-y+1/2,x+5/4,-z+1/4;y+3/4,x+3/4,z+1/2;-y+1/2,-x+1/2,z;x+3/4,-y,z+3/4;-x+1/2,y+5/4,z+1/4;x+1/2,y,z+1/2;-x+1/4,-y+3/4,z;-y+3/4,x,z+3/4;y+1/2,-x+5/4,z+1/4;-y+1/4,-x+3/4,-z;y+1/2,x,-z+1/2;-x+3/4,y,-z+3/4;x+1/2,-y+5/4,-z+1/4;-x+1/2,-y,-z+1/2;x+1/4,y+3/4,-z;y+1/4,-x,-z+1/4;-y+1/2,x+3/4,-z+3/4;y+1/4,x+3/4,z;-y+1/2,-x,z+1/2;x+1/4,-y,z+1/4;-x+1/2,y+3/4,z+3/4", // ITA 141.2 "141:1;141.3;a,b,c|0,1/4,-1/8;32;d4h^19;i 41/a m d :1;i 4bw 2bw -1bw", "141:f1;141.4;ab|0,1/4,-1/8;64;d4h^19;f 41/d d m :1;xyz",//;x,y,z;-x+1/2,-y,z+1/2;-y+3/4,x+1/4,z+1/4;y+1/4,-x+1/4,z+3/4;-y+1/4,-x+1/4,-z+3/4;y+1/4,x+3/4,-z+1/4;-x,y+1/2,-z+1/2;x,-y,-z;-x+1/4,-y+3/4,-z+1/4;x+1/4,y+1/4,-z+3/4;y+1/2,-x+1/2,-z;-y,x+1/2,-z+1/2;y+1/2,x,z+1/2;-y,-x,z;x+1/4,-y+1/4,z+3/4;-x+1/4,y+3/4,z+1/4;x,y+1/2,z+1/2;-x,-y,z;-y+1/4,x+1/4,z+3/4;y+1/4,-x+3/4,z+1/4;-y+3/4,-x+1/4,-z+1/4;y+1/4,x+1/4,-z+3/4;-x+1/2,y+1/2,-z;x,-y+1/2,-z+1/2;-x+1/4,-y+1/4,-z+3/4;x+3/4,y+1/4,-z+1/4;y,-x+1/2,-z+1/2;-y,x,-z;y,x,z;-y,-x+1/2,z+1/2;x+3/4,-y+1/4,z+1/4;-x+1/4,y+1/4,z+3/4;x+1/2,y+1/2,z;-x,-y+1/2,z+1/2;-y+1/4,x+3/4,z+1/4;y+3/4,-x+3/4,z+3/4;-y+3/4,-x+3/4,-z+3/4;y+3/4,x+1/4,-z+1/4;-x+1/2,y,-z+1/2;x+1/2,-y+1/2,-z;-x+3/4,-y+1/4,-z+1/4;x+3/4,y+3/4,-z+3/4;y,-x,-z;-y+1/2,x,-z+1/2;y,x+1/2,z+1/2;-y+1/2,-x+1/2,z;x+3/4,-y+3/4,z+3/4;-x+3/4,y+5/4,z+1/4;x+1/2,y,z+1/2;-x+1/2,-y+1/2,z;-y+3/4,x+3/4,z+3/4;y+3/4,-x+5/4,z+1/4;-y+1/4,-x+3/4,-z+1/4;y+3/4,x+3/4,-z+3/4;-x,y,-z;x+1/2,-y,-z+1/2;-x+3/4,-y+3/4,-z+3/4;x+1/4,y+3/4,-z+1/4;y+1/2,-x,-z+1/2;-y+1/2,x+1/2,-z;y+1/2,x+1/2,z;-y+1/2,-x,z+1/2;x+1/4,-y+3/4,z+1/4;-x+3/4,y+3/4,z+3/4", // ITA 141.4 "142:2;142.1;;32;d4h^20;i 41/a c d :2;-i 4bd 2c", "142:f2;142.2;ab;64;d4h^20;f 41/d d c :2;xyz",//;x,y,z;-x+1/4,-y+1/4,z+1/2;-y+3/4,x+1/2,z+1/4;y,-x+1/4,z+3/4;-y+1/4,-x+1/4,-z;y,x,-z+1/2;-x+3/4,y+1/2,-z+3/4;x,-y+1/4,-z+1/4;-x,-y,-z;x+1/4,y+1/4,-z+1/2;y+1/4,-x+1/2,-z+3/4;-y,x+3/4,-z+1/4;y+1/4,x+1/4,z;-y,-x,z+1/2;x+1/4,-y+1/2,z+1/4;-x,y+3/4,z+3/4;x,y+1/2,z+1/2;-x+3/4,-y+1/4,z;-y+1/4,x+1/2,z+3/4;y,-x+3/4,z+1/4;-y+3/4,-x+1/4,-z+1/2;y,x+1/2,-z;-x+1/4,y+1/2,-z+1/4;x,-y+3/4,-z+3/4;-x,-y+1/2,-z+1/2;x+3/4,y+1/4,-z;y+3/4,-x+1/2,-z+1/4;-y,x+1/4,-z+3/4;y+3/4,x+1/4,z+1/2;-y,-x+1/2,z;x+3/4,-y+1/2,z+3/4;-x,y+1/4,z+1/4;x+1/2,y+1/2,z;-x+3/4,-y+3/4,z+1/2;-y+1/4,x,z+1/4;y+1/2,-x+3/4,z+3/4;-y+3/4,-x+3/4,-z;y+1/2,x+1/2,-z+1/2;-x+1/4,y,-z+3/4;x+1/2,-y+3/4,-z+1/4;-x+1/2,-y+1/2,-z;x+3/4,y+3/4,-z+1/2;y+3/4,-x,-z+3/4;-y+1/2,x+5/4,-z+1/4;y+3/4,x+3/4,z;-y+1/2,-x+1/2,z+1/2;x+3/4,-y,z+1/4;-x+1/2,y+5/4,z+3/4;x+1/2,y,z+1/2;-x+1/4,-y+3/4,z;-y+3/4,x,z+3/4;y+1/2,-x+5/4,z+1/4;-y+1/4,-x+3/4,-z+1/2;y+1/2,x,-z;-x+3/4,y,-z+1/4;x+1/2,-y+5/4,-z+3/4;-x+1/2,-y,-z+1/2;x+1/4,y+3/4,-z;y+1/4,-x,-z+1/4;-y+1/2,x+3/4,-z+3/4;y+1/4,x+3/4,z+1/2;-y+1/2,-x,z;x+1/4,-y,z+3/4;-x+1/2,y+3/4,z+1/4", // ITA 142.2 "142:1;142.3;a,b,c|0,1/4,-1/8;32;d4h^20;i 41/a c d :1;i 4bw 2aw -1bw", "142:f1;142.4;ab|0,1/4,-1/8;64;d4h^20;f 41/d d c :1;xyz",//;x,y,z;-x+1/2,-y,z+1/2;-y+3/4,x+1/4,z+1/4;y+1/4,-x+1/4,z+3/4;-y+1/4,-x+1/4,-z+1/4;y+1/4,x+3/4,-z+3/4;-x,y+1/2,-z;x,-y,-z+1/2;-x+1/4,-y+3/4,-z+1/4;x+1/4,y+1/4,-z+3/4;y+1/2,-x+1/2,-z;-y,x+1/2,-z+1/2;y+1/2,x,z;-y,-x,z+1/2;x+1/4,-y+1/4,z+1/4;-x+1/4,y+3/4,z+3/4;x,y+1/2,z+1/2;-x,-y,z;-y+1/4,x+1/4,z+3/4;y+1/4,-x+3/4,z+1/4;-y+3/4,-x+1/4,-z+3/4;y+1/4,x+1/4,-z+1/4;-x+1/2,y+1/2,-z+1/2;x,-y+1/2,-z;-x+1/4,-y+1/4,-z+3/4;x+3/4,y+1/4,-z+1/4;y,-x+1/2,-z+1/2;-y,x,-z;y,x,z+1/2;-y,-x+1/2,z;x+3/4,-y+1/4,z+3/4;-x+1/4,y+1/4,z+1/4;x+1/2,y+1/2,z;-x,-y+1/2,z+1/2;-y+1/4,x+3/4,z+1/4;y+3/4,-x+3/4,z+3/4;-y+3/4,-x+3/4,-z+1/4;y+3/4,x+1/4,-z+3/4;-x+1/2,y,-z;x+1/2,-y+1/2,-z+1/2;-x+3/4,-y+1/4,-z+1/4;x+3/4,y+3/4,-z+3/4;y,-x,-z;-y+1/2,x,-z+1/2;y,x+1/2,z;-y+1/2,-x+1/2,z+1/2;x+3/4,-y+3/4,z+1/4;-x+3/4,y+5/4,z+3/4;x+1/2,y,z+1/2;-x+1/2,-y+1/2,z;-y+3/4,x+3/4,z+3/4;y+3/4,-x+5/4,z+1/4;-y+1/4,-x+3/4,-z+3/4;y+3/4,x+3/4,-z+1/4;-x,y,-z+1/2;x+1/2,-y,-z;-x+3/4,-y+3/4,-z+3/4;x+1/4,y+3/4,-z+1/4;y+1/2,-x,-z+1/2;-y+1/2,x+1/2,-z;y+1/2,x+1/2,z+1/2;-y+1/2,-x,z;x+1/4,-y+3/4,z+3/4;-x+3/4,y+3/4,z+1/4", // ITA 142.4 "143;143.1;;3;c3^1;p 3;p 3", "144;144.1;;3;c3^2;p 31;p 31", "145;145.1;;3;c3^3;p 32;p 32", "146:h;146.1;;9;c3^4;r 3 :h;r 3", "146:r;146.2;r;3;c3^4;r 3 :r;p 3*", "147;147.1;;6;c3i^1;p -3;-p 3", "148:h;148.1;;18;c3i^2;r -3 :h;-r 3", "148:r;148.2;r;6;c3i^2;r -3 :r;-p 3*", "149;149.1;;6;d3^1;p 3 1 2;p 3 2", "150;150.1;;6;d3^2;p 3 2 1;p 3 2\"", "151;151.1;;6;d3^3;p 31 1 2;p 31 2 (0 0 4)", "152;152.1;;6;d3^4;p 31 2 1;p 31 2\"", "152:_2;152:a,b,c|0,0,-1/3;a,b,c|0,0,-1/3;6;d3^4;p 31 2 1;p 31 2\" (0 0 -4)", // NOTE: MSA quartz.cif gives different operators for this -- "153;153.1;;6;d3^5;p 32 1 2;p 32 2 (0 0 2)", "154;154.1;;6;d3^6;p 32 2 1;p 32 2\"", "154:_2;154:a,b,c|0,0,-1/3;a,b,c|0,0,-1/3;6;d3^6;p 32 2 1;p 32 2\" (0 0 4)", // NOTE: MSA quartz.cif gives different operators for this -- "155:h;155.1;;18;d3^7;r 3 2 :h;r 3 2\"", "155:r;155.2;r;6;d3^7;r 3 2 :r;p 3* 2", "156;156.1;;6;c3v^1;p 3 m 1;p 3 -2\"", "157;157.1;;6;c3v^2;p 3 1 m;p 3 -2", "158;158.1;;6;c3v^3;p 3 c 1;p 3 -2\"c", "159;159.1;;6;c3v^4;p 3 1 c;p 3 -2c", "160:h;160.1;;18;c3v^5;r 3 m :h;r 3 -2\"", "160:r;160.2;r;6;c3v^5;r 3 m :r;p 3* -2", "161:h;161.1;;18;c3v^6;r 3 c :h;r 3 -2\"c", "161:r;161.2;r;6;c3v^6;r 3 c :r;p 3* -2n", "162;162.1;;12;d3d^1;p -3 1 m;-p 3 2", "163;163.1;;12;d3d^2;p -3 1 c;-p 3 2c", "164;164.1;;12;d3d^3;p -3 m 1;-p 3 2\"", "165;165.1;;12;d3d^4;p -3 c 1;-p 3 2\"c", "166:h;166.1;;36;d3d^5;r -3 m :h;-r 3 2\"", "166:r;166.2;r;12;d3d^5;r -3 m :r;-p 3* 2", "167:h;167.1;;36;d3d^6;r -3 c :h;-r 3 2\"c", "167:r;167.2;r;12;d3d^6;r -3 c :r;-p 3* 2n", "168;168.1;;6;c6^1;p 6;p 6", "169;169.1;;6;c6^2;p 61;p 61", "170;170.1;;6;c6^3;p 65;p 65", "171;171.1;;6;c6^4;p 62;p 62", "172;172.1;;6;c6^5;p 64;p 64", "173;173.1;;6;c6^6;p 63;p 6c", //"173*;173.1;;6;c6^6;p 63*;p 63 ", //nonstandard",// space added so not identical to H-M P 63 "174;174.1;;6;c3h^1;p -6;p -6", "175;175.1;;12;c6h^1;p 6/m;-p 6", "176;176.1;;12;c6h^2;p 63/m;-p 6c", //"176*;176.1;;12;c6h^2;p 63/m*;-p 63", //nonstandard "177;177.1;;12;d6^1;p 6 2 2;p 6 2", "178;178.1;;12;d6^2;p 61 2 2;p 61 2 (0 0 5)", "179;179.1;;12;d6^3;p 65 2 2;p 65 2 (0 0 1)", "180;180.1;;12;d6^4;p 62 2 2;p 62 2 (0 0 4)", "181;181.1;;12;d6^5;p 64 2 2;p 64 2 (0 0 2)", "182;182.1;;12;d6^6;p 63 2 2;p 6c 2c", //"182*;182.1;;12;d6^6;p 63 2 2*;p 63 2c", //nonstandard "183;183.1;;12;c6v^1;p 6 m m;p 6 -2", "184;184.1;;12;c6v^2;p 6 c c;p 6 -2c", "185;185.1;;12;c6v^3;p 63 c m;p 6c -2", //"185*;185.1;;12;c6v^3;p 63 c m*;p 63 -2", //nonstandard "186;186.1;;12;c6v^4;p 63 m c;p 6c -2c", //"186*;186.1;;12;c6v^4;p 63 m c*;p 63 -2c", //nonstandard "187;187.1;;12;d3h^1;p -6 m 2;p -6 2", "188;188.1;;12;d3h^2;p -6 c 2;p -6c 2", "189;189.1;;12;d3h^3;p -6 2 m;p -6 -2", "190;190.1;;12;d3h^4;p -6 2 c;p -6c -2c", "191;191.1;;24;d6h^1;p 6/m m m;-p 6 2", "192;192.1;;24;d6h^2;p 6/m c c;-p 6 2c", "193;193.1;;24;d6h^3;p 63/m c m;-p 6c 2", //"193*;193.1;;24;d6h^3;p 63/m c m*;-p 63 2", //nonstandard "194;194.1;;24;d6h^4;p 63/m m c;-p 6c 2c", //"194*;194.1;;24;d6h^4;p 63/m m c*;-p 63 2c", //nonstandard "195;195.1;;12;t^1;p 2 3;p 2 2 3", "196;196.1;;48;t^2;f 2 3;f 2 2 3", "197;197.1;;24;t^3;i 2 3;i 2 2 3", "198;198.1;;12;t^4;p 21 3;p 2ac 2ab 3", "199;199.1;;24;t^5;i 21 3;i 2b 2c 3", "200;200.1;;24;th^1;p m -3;-p 2 2 3", "201:2;201.1;;24;th^2;p n -3 :2;-p 2ab 2bc 3", "201:1;201.2;a,b,c|-1/4,-1/4,-1/4;24;th^2;p n -3 :1;p 2 2 3 -1n", "202;202.1;;96;th^3;f m -3;-f 2 2 3", "203:2;203.1;;96;th^4;f d -3 :2;-f 2uv 2vw 3", "203:1;203.2;a,b,c|-1/8,-1/8,-1/8;96;th^4;f d -3 :1;f 2 2 3 -1d", "204;204.1;;48;th^5;i m -3;-i 2 2 3", "205;205.1;;24;th^6;p a -3;-p 2ac 2ab 3", "206;206.1;;48;th^7;i a -3;-i 2b 2c 3", "207;207.1;;24;o^1;p 4 3 2;p 4 2 3", "208;208.1;;24;o^2;p 42 3 2;p 4n 2 3", "209;209.1;;96;o^3;f 4 3 2;f 4 2 3", "210;210.1;;96;o^4;f 41 3 2;f 4d 2 3", "211;211.1;;48;o^5;i 4 3 2;i 4 2 3", "212;212.1;;24;o^6;p 43 3 2;p 4acd 2ab 3", "213;213.1;;24;o^7;p 41 3 2;p 4bd 2ab 3", "214;214.1;;48;o^8;i 41 3 2;i 4bd 2c 3", "215;215.1;;24;td^1;p -4 3 m;p -4 2 3", "216;216.1;;96;td^2;f -4 3 m;f -4 2 3", "217;217.1;;48;td^3;i -4 3 m;i -4 2 3", "218;218.1;;24;td^4;p -4 3 n;p -4n 2 3", "219;219.1;;96;td^5;f -4 3 c;f -4a 2 3", "220;220.1;;48;td^6;i -4 3 d;i -4bd 2c 3", "221;221.1;;48;oh^1;p m -3 m;-p 4 2 3", "222:2;222.1;;48;oh^2;p n -3 n :2;-p 4a 2bc 3", "222:1;222.2;a,b,c|-1/4,-1/4,-1/4;48;oh^2;p n -3 n :1;p 4 2 3 -1n", "223;223.1;;48;oh^3;p m -3 n;-p 4n 2 3", "224:2;224.1;;48;oh^4;p n -3 m :2;-p 4bc 2bc 3", "224:1;224.2;a,b,c|-1/4,-1/4,-1/4;48;oh^4;p n -3 m :1;p 4n 2 3 -1n", "225;225.1;;192;oh^5;f m -3 m;-f 4 2 3", "226;226.1;;192;oh^6;f m -3 c;-f 4a 2 3", "227:2;227.1;;192;oh^7;f d -3 m :2;-f 4vw 2vw 3", "227:1;227.2;a,b,c|-1/8,-1/8,-1/8;192;oh^7;f d -3 m :1;f 4d 2 3 -1d", "228:2;228.1;;192;oh^8;f d -3 c :2;-f 4ud 2vw 3", "228:1;228.2;a,b,c|-3/8,-3/8,-3/8;192;oh^8;f d -3 c :1;f 4d 2 3 -1ad", "229;229.1;;96;oh^9;i m -3 m;-i 4 2 3", "230;230.1;;96;oh^10;i a -3 d;-i 4bd 2c 3", }; // first HM entry (short) is saved in ClegToHM private final static String[] moreSettings = { // these are allowed only in their full-name form, with a "'" following "A 1 1 2 :2'","5:-a-c,a,-b", "A 1 2 1 :1'","5:c,-b,a", "B 1 1 2 :1'","5:a,c,-b", "B 2 1 1 :2'","5:-b,-a-c,a", "C 1 2 1 :2'","5:a,-b,-a-c", "C 2 1 1 :1'","5:-b,a,c", "I 1 1 2 :3'","5:c,-a-c,-b", "I 1 2 1 :3'","5:-a-c,-b,c", "I 2 1 1 :3'","5:-b,c,-a-c", "P 1 1 a :3'","7:c,-a-c,-b", "P 1 1 b :1'","7:a,c,-b", "P 1 1 n :2'","7:-a-c,a,-b", "P 1 a 1 :1'","7:c,-b,a", "P 1 c 1 :3'","7:-a-c,-b,c", "P 1 n 1 :2'","7:a,-b,-a-c", "P b 1 1 :3'","7:-b,c,-a-c", "P c 1 1 :1'","7:-b,a,c", "P n 1 1 :2'","7:-b,-a-c,a", "A 1 1 m :2'","8:-a-c,a,-b", "A 1 m 1 :1'","8:c,-b,a", "B 1 1 m :1'","8:a,c,-b", "B m 1 1 :2'","8:-b,-a-c,a", "C 1 m 1 :2'","8:a,-b,-a-c", "C m 1 1 :1'","8:-b,a,c", "I 1 1 m :3'","8:c,-a-c,-b", "I 1 m 1 :3'","8:-a-c,-b,c", "I m 1 1 :3'","8:-b,c,-a-c", "A 1 1 2/m :2'","12:-a-c,a,-b", "A 1 2/m 1 :1'","12:c,-b,a", "B 1 1 2/m :1'","12:a,c,-b", "B 2/m 1 1 :2'","12:-b,-a-c,a", "C 1 2/m 1 :2'","12:a,-b,-a-c", "C 2/m 1 1 :1'","12:-b,a,c", "I 1 1 2/m :3'","12:c,-a-c,-b", "I 1 2/m 1 :3'","12:-a-c,-b,c", "I 2/m 1 1 :3'","12:-b,c,-a-c", "P 1 1 2/a :3'","13:c,-a-c,-b", "P 1 1 2/b :1'","13:a,c,-b", "P 1 1 2/n :2'","13:-a-c,a,-b", "P 1 2/a 1 :1'","13:c,-b,a", "P 1 2/c 1 :3'","13:-a-c,-b,c", "P 1 2/n 1 :2'","13:a,-b,-a-c", "P 2/b 1 1 :3'","13:-b,c,-a-c", "P 2/c 1 1 :1'","13:-b,a,c", "P 2/n 1 1 :2'","13:-b,-a-c,a", "P 1 1 21/a :3'","14:c,-a-c,-b", "P 1 1 21/b :1'","14:a,c,-b", "P 1 1 21/n :2'","14:-a-c,a,-b", "P 1 21/a 1 :1'","14:c,-b,a", "P 1 21/c 1 :3'","14:-a-c,-b,c", "P 1 21/n 1 :2'","14:a,-b,-a-c", "P 21/b 1 1 :3'","14:-b,c,-a-c", "P 21/c 1 1 :1'","14:-b,a,c", "P 21/n 1 1 :2'","14:-b,-a-c,a", "C 4'","75:a+b,-a+b,c", "C 41'","76:a+b,-a+b,c", "C 42'","77:a+b,-a+b,c", "C 43'","78:a+b,-a+b,c", "F 4'","79:a+b,-a+b,c", "F 41'","80:a+b,-a+b,c", "C -4'","81:a+b,-a+b,c", "F -4'","82:a+b,-a+b,c", "C 4/m'","83:a+b,-a+b,c", "C 42/m'","84:a+b,-a+b,c", "C 4/e :1'","85:a+b,-a+b,c;-1/4,1/4,0", "C 4/e :2'","85:a+b,-a+b,c", "C 42/e :1'","86:a+b,-a+b,c;-1/4,-1/4,-1/4", "C 42/e :2'","86:a+b,-a+b,c", "F 4/m'","87:a+b,-a+b,c", "F 41/d :1'","88:a+b,-a+b,c;0,-1/4,-1/8", "F 41/d :2'","88:a+b,-a+b,c", "C 4 2 2'","89:a+b,-a+b,c", "C 4 2 21'","90:a+b,-a+b,c", "C 41 2 2'","91:a+b,-a+b,c", "C 41 2 21'","92:a+b,-a+b,c", "C 42 2 2'","93:a+b,-a+b,c", "C 42 2 21'","94:a+b,-a+b,c", "C 43 2 2'","95:a+b,-a+b,c", "C 43 2 21'","96:a+b,-a+b,c", "F 4 2 2'","97:a+b,-a+b,c", "F 41 2 2'","98:a+b,-a+b,c", "C 4 m m'","99:a+b,-a+b,c", "C 4 m g1'","100:a+b,-a+b,c", "C 42 m c'","101:a+b,-a+b,c", "C 42 m g2'","102:a+b,-a+b,c", "C 4 c c'","103:a+b,-a+b,c", "C 4 c g2'","104:a+b,-a+b,c", "C 42 c m'","105:a+b,-a+b,c", "C 42 c g1'","106:a+b,-a+b,c", "F 4 m m'","107:a+b,-a+b,c", "F 4 m c'","108:a+b,-a+b,c", "F 41 d m'","109:a+b,-a+b,c", "F 41 d c'","110:a+b,-a+b,c", "C -4 m 2'","111:a+b,-a+b,c", "C -4 c 2'","112:a+b,-a+b,c", "C -4 m 21'","113:a+b,-a+b,c", "C -4 c 21'","114:a+b,-a+b,c", "C -4 2 m'","115:a+b,-a+b,c", "C -4 2 c'","116:a+b,-a+b,c", "C -4 2 g1'","117:a+b,-a+b,c", "C -4 2 g2'","118:a+b,-a+b,c", "F -4 2 m'","119:a+b,-a+b,c", "F -4 2 c'","120:a+b,-a+b,c", "F -4 m 2'","121:a+b,-a+b,c", "F -4 d 2'","122:a+b,-a+b,c", "C 4/m m m'","123:a+b,-a+b,c", "C 4/m c c'","124:a+b,-a+b,c", "C 4/e m g1 :1'","125:a+b,-a+b,c;-1/4,-1/4,0", "C 4/e m g1 :2'","125:a+b,-a+b,c", "C 4/e c g2 :1'","126:a+b,-a+b,c;-1/4,-1/4,-1/4", "C 4/e c g2 :2'","126:a+b,-a+b,c", "C 4/m m g1'","127:a+b,-a+b,c", "C 4/m c g2'","128:a+b,-a+b,c", "C 4/e m m :1'","129:a+b,-a+b,c;-1/4,1/4,0", "C 4/e m m :2'","129:a+b,-a+b,c", "C 4/e c c :1'","130:a+b,-a+b,c;-1/4,1/4,0", "C 4/e c c :2'","130:a+b,-a+b,c", "C 42/m c m'","131:a+b,-a+b,c", "C 42/m m c'","132:a+b,-a+b,c", "C 42/e c g1 :1'","133:a+b,-a+b,c;-1/4,1/4,-1/4", "C 42/e c g1 :2'","133:a+b,-a+b,c", "C 42/e m g2 :1'","134:a+b,-a+b,c;-1/4,1/4,-1/4", "C 42/e m g2 :2'","134:a+b,-a+b,c", "C 42/m c g1'","135:a+b,-a+b,c", "C 42/m m g2'","136:a+b,-a+b,c", "C 42/e c m :1'","137:a+b,-a+b,c;-1/4,1/4,-1/4", "C 42/e c m :2'","137:a+b,-a+b,c", "C 42/e m c :1'","138:a+b,-a+b,c;-1/4,1/4,-1/4", "C 42/e m c :2'","138:a+b,-a+b,c", "F 4/m m m'","139:a+b,-a+b,c", "F 4/m m c'","140:a+b,-a+b,c", "F 41/d d m :1'","141:a+b,-a+b,c;0,1/4,-1/8", "F 41/d d m :2'","141:a+b,-a+b,c", "F 41/d d c :1'","142:a+b,-a+b,c;0,1/4,-1/8", "F 41/d d c :2'","142:a+b,-a+b,c", }; private static Hashtable HMtoCleg; private static Hashtable ClegtoHM; /** * Convert short or full HM names to CLEG; CLEG to short HM name. * Possibly little use for CLEG to HM. * * @param hmName * @param cleg * @return equivalent name or null */ static String convertWyckoffHMCleg(String hmName, String cleg) { if (HMtoCleg == null) { HMtoCleg = new Hashtable<>(); ClegtoHM = new Hashtable<>(); for (int i = moreSettings.length; --i >= 0;) { String c = moreSettings[i]; String h = moreSettings[--i]; h = PT.rep(h, " ",""); ClegtoHM.put(c, h); HMtoCleg.put(h, c); } } return (hmName != null ? HMtoCleg.get(PT.rep(hmName, " ","")) : ClegtoHM.get(cleg)); } public String getHMName() { return hmSymbol; } public static int getITNo(String name, int n) { if (n <= 0) n = name.length(); for (int i = n; --i >= 0;) if (!PT.isDigit(name.charAt(i))) return -1; return Integer.parseInt(name.substring(0, n)); } public static boolean isInRange(float itno, int groupType, boolean allowSetIndex, boolean allow300) { int max = getMax(groupType); switch (groupType) { case TYPE_SPACE: if (allow300) { int i = (int) itno; int type = getImplicitSpecialGroupType(i); if (type == TYPE_PLANE) allowSetIndex = false; return (type != TYPE_INVALID && (allowSetIndex || i == itno)); } break; case TYPE_PLANE: allowSetIndex = false; break; case TYPE_LAYER: case TYPE_ROD: case TYPE_FRIEZE: break; } // possibly for 230.1 230.2, etc return itno >= 1 && (allowSetIndex ? itno < max + 1 : itno <= max); } public static int getMax(int groupType) { switch (groupType) { case TYPE_SPACE: return 230; case TYPE_PLANE: return 17; case TYPE_LAYER: return 80; case TYPE_ROD: return 75; case TYPE_FRIEZE: return 7; default: return 0; } } public static String getGroupTypePrefix(int itno) { itno -= itno % 100; switch (itno) { case TYPE_SPACE: return PREFIX_SPACE; case TYPE_PLANE: return PREFIX_PLANE; case TYPE_LAYER: return PREFIX_LAYER; case TYPE_ROD: return PREFIX_ROD; case TYPE_FRIEZE: return PREFIX_FRIEZE; } return ""; } public static int getExplicitSpecialGroupType(String name) { if (name.length() < 2 || name.charAt(1) != '/') return TYPE_SPACE; switch (name.substring(0,2)) { case PREFIX_PLANE: return TYPE_PLANE; case PREFIX_LAYER: return TYPE_LAYER; case PREFIX_ROD: return TYPE_ROD; case PREFIX_FRIEZE: return TYPE_FRIEZE; default: return TYPE_INVALID; } } public static String getSpecialGroupName(int type) { switch (type) { case TYPE_SPACE: return ""; case TYPE_PLANE: return "plane"; case TYPE_LAYER: return "layer"; case TYPE_ROD: return "rod"; case TYPE_FRIEZE: return "frieze"; default: return null; } } public static int getImplicitSpecialGroupType(int itno) { if (itno < 1) return TYPE_INVALID; if (itno <= 230) return TYPE_SPACE; if (itno > TYPE_PLANE && itno <= TYPE_PLANE + 17) return TYPE_PLANE; if (itno > TYPE_LAYER && itno <= TYPE_LAYER + 80) return TYPE_LAYER; if (itno > TYPE_ROD && itno <= TYPE_ROD + 75) return TYPE_ROD; if (itno > TYPE_FRIEZE && itno <= TYPE_FRIEZE + 7) return TYPE_FRIEZE; return TYPE_INVALID; } /** * Matches Hermann-Mauguin names for special types by * ignoring spaces and some special treatment for plane groups. * * @param hm * @param name * @param type * @return true if equivalent */ public static boolean hmEquals(String hm, String name, int type) { if (hm.charAt(1) == '/') hm = hm.substring(2); if (hm.charAt(0) != name.charAt(0)) return false; if (name.indexOf(' ') < 0) { hm = PT.rep(hm, " ", ""); } if (hm.equals(name)) return true; if (type == TYPE_PLANE) { int n = hm.length(); if (n <= name.length()) return false; char c = name.charAt(1); switch (name.length()) { case 2: // p1m1 p1g1 c1m1 // accepts pm pg cm return (n == 4 && hm.charAt(1) == '1' && c == hm.charAt(2)); case 3: // p2mm p2mg p2gg c2mm // accepts pmm pmg pgg cmm // p4mm p4gm p6mm // accepts p4m p4g p6m char c2 = hm.charAt(1); return (c2 == '2' ? hm.charAt(2) == c && hm.charAt(3) == name.charAt(2) : hm.charAt(n - 1) == 'm' && hm.startsWith(name)); } } return false; } /** * Create a unit cell compatible with * * @param params * @param newParams * @param allowSame * true to allow same-distance a,b,c for lower-symmetry sg * @return true if changes have occurred */ public boolean createCompatibleUnitCell(float[] params, float[] newParams, boolean allowSame) { if (newParams == null) newParams = params; float a = params[0]; float b = params[1]; float c = params[2]; float alpha = params[3]; float beta = params[4]; float gamma = params[5]; int n = (itaNumber == null ? 0 : PT.parseInt(itaNumber)); boolean toHex = false, isHex = false, toRhom = false, isRhom = false; toHex = (n != 0 && isHexagonalSG(n, null)); isHex = (toHex && isHexagonalSG(-1, params)); toRhom = (n != 0 && axisChoice == 'r'); isRhom = (toRhom && SimpleUnitCell.isRhombohedral(params)); if (toHex && isHex || toRhom && isRhom) { allowSame = true; } if (n > (allowSame ? 2 : 0)) { boolean absame = b > 0 && SimpleUnitCell.approx0(a - b); boolean bcsame = c > 0 && SimpleUnitCell.approx0(b - c); boolean acsame = c > 0 && SimpleUnitCell.approx0(c - a); boolean albesame = SimpleUnitCell.approx0(alpha - beta); boolean begasame = SimpleUnitCell.approx0(beta - gamma); boolean algasame = SimpleUnitCell.approx0(gamma - alpha); if (!allowSame) { // make a, b, and c all distinct if (b > 0 && a > b) { float d = a; a = b; b = d; } bcsame = c > 0 && SimpleUnitCell.approx0(b - c); if (bcsame) c = b * 1.5f; absame = SimpleUnitCell.approx0(a - b); if (absame) b = a * 1.2f; acsame = SimpleUnitCell.approx0(c - a); if (acsame) c = a * 1.1f; // make alpha, beta, and gamma all distinct if (SimpleUnitCell.approx0(alpha - 90)) { alpha = 80; } if (SimpleUnitCell.approx0(beta - 90)) { beta = 100; } if (SimpleUnitCell.approx0(gamma - 90)) { gamma = 110; } if (alpha > beta) { float d = alpha; alpha = beta; beta = d; } albesame = SimpleUnitCell.approx0(alpha - beta); begasame = SimpleUnitCell.approx0(beta - gamma); algasame = SimpleUnitCell.approx0(gamma - alpha); if (albesame) { beta = alpha * 1.2f; } if (begasame) { gamma = beta * 1.3f; } if (algasame) { gamma = alpha * 1.4f; } } if (toHex) { if (toRhom ? isRhom : isHex) { // nothing to do } else if (axisChoice == 'r') { c = b = a; if (!allowSame && alpha > 85 && alpha < 95) alpha = 80; gamma = beta = alpha; } else { b = a; alpha = beta = 90; gamma = 120; } } else if (n >= 195) { // cubic c = b = a; alpha = beta = gamma = 90; } else if (n >= 75) { // tetragonal b = a; if (acsame && !allowSame) c = a * 1.5f; alpha = beta = gamma = 90; } else if (n >= 16) { // orthorhombic alpha = beta = gamma = 90; } else if (n >= 3) { // monoclinic switch (uniqueAxis) { case 'a': beta = gamma = 90; break; default: case 'b': alpha = gamma = 90; break; case 'c': alpha = beta = 90; break; } } } boolean isNew = !(a == params[0] && b == params[1] && c == params[2] && alpha == params[3] && beta == params[4] && gamma == params[5]); newParams[0] = a; newParams[1] = b; newParams[2] = c; newParams[3] = alpha; newParams[4] = beta; newParams[5] = gamma; return isNew; } public boolean isHexagonalSG(int n, float[] params) { return (n < 1 ? SimpleUnitCell.isHexagonal(params) : n >= 143 && n <= 194); } // public boolean isMonoclinicSG(int n) { // return (n >= 3 && n <= 15); // } // // public boolean isTetragonalSG(int n) { // return (n >= 75 && n <= 142); // } // // public static boolean isPolarSG(int n) { // return ( n == 1 // 1 // || n >= 3 && n <= 5 // 2 // || n >= 6 && n <= 9 // m // || n >= 25 && n <= 46 // 2mm // || n >= 75 && n <= 80 // 4 // || n >= 99 && n <= 110 // 4mm // || n >= 143 && n <= 146 // 3 // || n >= 156 && n <= 161 // 3mm // || n >= 168 && n <= 173 // 6 // || n >= 183 && n <= 186 // 6mm // ); // } // static { getSpaceGroups(); } }