XPDFSpaceGroup.java

/*
 * Copyright 2016 Diamond Light Source Ltd.
 *
 * All rights reserved. This program and the accompanying materials
 * are made available under the terms of the Eclipse Public License v1.0
 * which accompanies this distribution, and is available at
 * http://www.eclipse.org/legal/epl-v10.html
 */

package uk.ac.diamond.scisoft.xpdf.views;

import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Set;
import java.util.regex.Pattern;

/**
 * Parameterizes the properties of crystal space groups.
 * <p>
 * Parameterizes the properties of the 230 space groups, and 7 additional
 * pseudo-groups parameterizing the rhombohedral basis for those trigonal space
 * groups.
 * @author Timothy Spain, timothy.spain@diamond.ac.uk
 *
 */
// TODO: give the rhombohedral based pseudo-groups their actual number at the interface.
class XPDFSpaceGroup {

	private int number;
	private static XPDFSpaceGroup[] groups;
	static final Integer[] rhombGroups = {146, 148, 155, 160, 161, 166, 167};
	static final int nGroupsFedorov = 230;
	static final int nGroups = nGroupsFedorov + rhombGroups.length;
	private static Map<Integer, Integer> hexagonalRhombohedralGroupMap = null;
	private WyckoffData wyckoffData;
	
	public static final String allWyckoffLetters = "abcdefghijklmnopqrstuvwxyzα"; 
	
	private static Pattern spacePattern = null;
	final static int base10 = 10;
	private static final String normalNumbers = "0123456789.";
	private static final String subscriptNumbers = "₀₁₂₃₄₅₆₇₈₉.";
	private static Pattern[] subscriptPatterns = null;
	private static Pattern overbarPattern = null;
	private static Pattern trueMinusPattern = null;
	private static Pattern hyphenMinusPattern = null;
	

	
	private XPDFSpaceGroup() {
	}
	
	/**
	 * Gets the space group with a given number.
	 * @param groupNumber
	 * 					number of the space group following the IUCr.
	 * @return the object representing that space group
	 */
	public static XPDFSpaceGroup get(int groupNumber) {
		if (groups == null) {
			generateGroups();
		}
		// Watch out for off by 1 errors
		return groups[groupNumber];
	}
	
	public static XPDFSpaceGroup get(String name) {
		// search long names, stripping spaces, converting subscripts to ASCII numerals, and overbars to leading hyphen-minuses
		String normalizedName = simplifyLongName(name);
		for (int iLongName = 1; iLongName < names.length; iLongName ++) {
			String normalizedLongName = simplifyLongName(names[iLongName]);
			if (normalizedLongName.equals(normalizedName))
				return get(iLongName);
		}
		
		normalizedName = simplifyShortName(name);
		for (int iShortName = 1; iShortName < shortNames.length; iShortName++) {
			String normalizedShortName = simplifyShortName(shortNames[iShortName]);
			if (normalizedShortName.equals(normalizedName))
				return get(iShortName);
		}
		// we have got here without finding a valid group. Has the writer of
		// the file forgotten to include a minus sign? Let's see. Only check
		// the short names in this case.
		String deminusedName = simplifyShortName(stripMinuses(name));
		for (int iShortName = 1; iShortName < shortNames.length; iShortName++) {
			String normalizedShortName = simplifyShortName(stripMinuses(shortNames[iShortName]));
			if (normalizedShortName.equals(deminusedName))
				return get(iShortName);
		}
		
		// return the null group
		return get(0);
	}
	
	/**
	 * Gets the number of a space group.
	 * @return
	 */
	public int getNumber() {
		return number;
	}
	
	/**
	 * Gets the symbolic name of the space group.
	 * @return the Hermann-Mauguin symbol of the space group.
	 */
	public String getName() {
		return names[number];
	}
	
	/**
	 * Gets the typical short form of the space group.
	 * @return the short-form Hermann-Maugin symbol of the space group.
	 */
	public String getShortName() {
		return shortNames[number];
	}
	
	/**
	 * Gets the object representing the crystal system of which this space
	 * group is a member 
	 * @return the {@link CrystalSystem} of the space group.
	 */
	public CrystalSystem getSystem() {
		if (number < 1)
			return null; // 0 is undefined
		else
			for (int iGroup = 0; iGroup < CrystalSystem.nSystems; iGroup++) {
				if (number <= CrystalSystem.highestGroups[iGroup])
					return CrystalSystem.get(iGroup);
			}
			return null; // system not found
	}
	
	/**
	 * Gets the symmetry operations of the space group.
	 * <p>
	 * Returns a list of Strings in the IUCr format describing all the
	 * transformations for an atom in the general position for the space group.
	 * The list is ordered such that the identity operation is always first.
	 * @return a list of Strings describing the symmetry operations
	 */
	public String[] getSymmetryOperations() {
		return allSymOps[number];
	}
	
	// Simplify the long form of a Hermann-Maugin name. Strip out spaces,
	// convert subscripts to ASCII numerals, convert overbars to leading
	// hyphen-minuses, convert Unicode minuses to hyphen-minuses
	private static String simplifyLongName(String name) {

		if (spacePattern == null)
			compilePatterns();

		// strip out all spaces
		String stripSpaces = simplifyShortName(name);
		// translate subscripts to ASCII
		String desubscript = stripSpaces;
		for (int i = 0; i < base10; i++)
			desubscript = subscriptPatterns[i].matcher(desubscript).replaceAll(Integer.toString(i));
		// convert overbars to hyphen-minuses
		String deoverbar = overbarPattern.matcher(desubscript).replaceAll("-$1");
		// convert real minuses to (ugh) hyphen-minuses
		String hyphenate = trueMinusPattern.matcher(deoverbar).replaceAll("-");
		
		return hyphenate;
	}
	
	// Simplify the short form of a Hermann-Maugin name. Strip out spaces
	private static String simplifyShortName(String name) {
		if (spacePattern == null) 
			compilePatterns();
		// strip out all spaces
		String stripSpaces = spacePattern.matcher(name).replaceAll("");
		
		return stripSpaces;
	}

	private static String stripMinuses(String name) {
		if (spacePattern == null)
			compilePatterns();
		return hyphenMinusPattern.matcher(name).replaceAll("");
	}
	
	private static void compilePatterns() {
		spacePattern = Pattern.compile(" +");
		subscriptPatterns = new Pattern[base10];
		for (int i = 0; i < base10; i++)
			subscriptPatterns[i] = Pattern.compile(Character.toString(subscriptNumbers.charAt(i)));
		overbarPattern = Pattern.compile("(\\p{Digit})\u0305");
		trueMinusPattern = Pattern.compile("\u2212");
		hyphenMinusPattern = Pattern.compile("-");
	}
	
	private static void generateGroups() {
		groups = new XPDFSpaceGroup[nGroups+1];
		for (int newGroup = 0; newGroup <= nGroups; newGroup++) {
			XPDFSpaceGroup group = new XPDFSpaceGroup();
			group.number = newGroup;
			group.wyckoffData = new WyckoffData(newGroup);
			groups[newGroup] = group;
		}
		
		// Also generate the mapping between rhombohedral and hexagonal groups
		hexagonalRhombohedralGroupMap = new HashMap<Integer, Integer>();
		for (int i = 0; i < nGroups-nGroupsFedorov; i++) {
			hexagonalRhombohedralGroupMap.put(rhombGroups[i], nGroupsFedorov+1+i);
			hexagonalRhombohedralGroupMap.put(nGroupsFedorov+1+i, rhombGroups[i]);
		}
	}
	
	/**
	 * Returns the rhombohedral equivalent space group.
	 * <p>
	 * If this is the space group has a rhombohedral lattice, then return the
	 * pseudo-space group representing its rhombohedral form. Otherwise, return this.
	 * @return
	 * 		the rhombohedral equivalent pseudo-space group, if it exists, else this.
	 */
	public XPDFSpaceGroup asRhombohedral() {
		if (this.hasRhombohedral()) {
			return groups[hexagonalRhombohedralGroupMap.get(number)];
		}
		return this;
	}
	
	/**
	 * Returns the hexagonal equivalent space group.
	 * <p>
	 * If this is a pseudo-space group of a rhombohedral lattice, then return the
	 * space group representing its hexagonal form. Otherwise, return this.
	 * @return
	 * 		the hexagonal equivalent space group, if it applicable, else this.
	 */
	public XPDFSpaceGroup asHexagonal() {
		if (this.isRhombohedral()) {
			return groups[hexagonalRhombohedralGroupMap.get(number)];
		}
		return this;
	}
	
	/**
	 * Returns whether the space group has an alternative rhombohedral basis
	 * @return
	 * 		does this space group have a rhombohedral basis, and is it itself in the hexagonal basis
	 */
	public boolean hasRhombohedral() {
		return Arrays.asList(rhombGroups).contains(this.number); 
	}
	
	/**
	 * Returns whether the space group is in a rhombohedral basis
	 * @return
	 * 		Returns whether the space group is a trigonal group represented in a rhombohedral basis 
	 */
	public boolean isRhombohedral() {
		return this.number > nGroupsFedorov;
	}
	
	public int getNWyckoffLetters() {
		return wyckoffData.getNLetters();
	}
	
	public int getSiteMultiplicity(String wyckoffLetter) {
		return wyckoffData.getMultiplicity(wyckoffLetter);
	}
	
	private static class WyckoffData {
		private final int nLetters;
		private int[] multiplicities;
		
		public WyckoffData(int spaceGroup) {
			nLetters = getNWyckoff(spaceGroup);
			multiplicities = getMultiplicity(spaceGroup);
		}
		
		public int getMultiplicity(String letter) {
			int letterIndex = indexFromLetter(letter);
			return multiplicities[letterIndex-1];
		}
		
		public int getNLetters() {
			return nLetters;
		}
		
		private static int indexFromLetter(String letter) {
			return ("?"+allWyckoffLetters).indexOf(letter.charAt(0));
		}
		
		private static String letterFromIndex(int index) {
			return Character.toString(("?"+allWyckoffLetters).charAt(index));
		}
		
		private static int getNWyckoff(int spaceGroup) {
			int[] nSpecial= {0, // null space group, for indexing
					 0, 8, 4, 0, 2, 2, 0, 1, 0, 14,
					 5, 9, 6, 4, 5, 20, 4, 2, 0, 2,
					 11, 10, 10, 3, 8, 2, 4, 3, 0, 2,
					 1, 2, 0, 2, 5, 1, 3, 5, 3, 2,
					 1, 4, 1, 4, 2, 2, 26, 12, 17, 12,
					 11, 4, 8, 5, 8, 4, 4, 7, 6, 3,
					 2, 3, 7, 6, 17, 12, 14, 8, 15, 7,
					 14, 10, 5, 9, 3, 0, 3, 0, 2, 1,
					 7, 6, 11, 10, 6, 6, 8, 5, 15, 6,
					 3, 1, 15, 6, 3, 1, 10, 6, 6, 3,
					 4, 3, 3, 2, 5, 2, 4, 3, 2, 1,
					 14, 13, 5, 4, 11, 9, 8, 8, 9, 8,
					 9, 4, 20, 13, 13, 10, 11, 8, 10, 6,
					 17, 15, 10, 13, 8, 10, 7, 9, 14, 12,
					 8, 6, 3, 0, 0, 1, 6, 5, 11, 6,
					 2, 2, 2, 2, 5, 4, 3, 3, 2, 2,
					 1, 11, 8, 9, 6, 8, 5, 3, 0, 0,
					 2, 2, 2, 11, 11, 8, 13, 2, 2, 10,
					 10, 8, 5, 3, 3, 3, 14, 11, 11, 8,
					 17, 12, 11, 11, 9, 7, 5, 1, 2, 11,
					 7, 8, 6, 7, 3, 4, 10, 12, 9, 7,
					 9, 4, 4, 8, 9, 8, 7, 8, 7, 4,
					 13, 8, 11, 11, 11, 9, 8, 7, 11, 7, // 230 real space groups
					 1, 5, 5, 2, 1, 8, 5}; // The rhombohedral pseudo-groups have the same number of special positions as the hexagonal representation
			return nSpecial[spaceGroup] + 1;
		}
		
		private static int[] getMultiplicity(int spaceGroup) {
			int[][] multiplicities = {
					{0}, // null group for indexing
					// 0-10
					{1},
					{1,1,1,1,1,1,1,1,2},
					{1,1,1,1,2},
					{2},
					{2,2,4},
					{1,1,2},
					{2},
					{2, 4},
					{4},
					{1,1,1,1,1,1,1,1,2,2,2,2,2,2,4},
					//11-20
					{2,2,2,2,2,4},
					{2,2,2,2,4,4,4,4,4,8},
					{2,2,2,2,2,2,4},
					{2,2,2,2,4},
					{4,4,4,4,4,8},
					{1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4},
					{2,2,2,2,4},
					{2,2,4},
					{4},
					{4,4,8},
					//21-30
					{2,2,2,2,4,4,4,4,4,4,4,8},
					{4,4,4,4,8,8,8,8,8,8,16},
					{2,2,2,2,4,4,4,4,4,4,8},
					{4,4,4,8},
					{1,1,1,1,2,2,2,2,4},
					{2,2,4},
					{2,2,2,2,4},
					{2,2,2,4},
					{4},
					{2,2,4},
					//31-40
					{2,4},
					{2,2,4},
					{4},
					{2,2,4},
					{2,2,4,4,4,8},
					{4,8},
					{4,4,4,8},
					{2,2,4,4,4,8},
					{4,4,4,8},
					{4,4,8},
					//41-50
					{4,8},
					{4,8,8,8,16},
					{8,16},
					{2,2,4,4,8},
					{4,4,8},
					{4,4,8},
					{1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,8},
					{2,2,2,2,4,4,4,4,4,4,4,4,8},
					{2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,8},
					{2,2,2,2,4,4,4,4,4,4,4,4,8},
					//51-60
					{2,2,2,2,2,2,4,4,4,4,4,8},
					{4,4,4,4,8},
					{2,2,2,2,4,4,4,4,8},
					{4,4,4,4,4,8},
					{2,2,2,2,4,4,4,4,8},
					{4,4,4,4,8},
					{4,4,4,4,8},
					{2,2,2,2,4,4,4,8},
					{2,2,4,4,4,4,8},
					{4,4,4,8},
					//61-70
					{4,4,8},
					{4,4,4,8},
					{4,4,4,8,8,8,8,16},
					{4,4,8,8,8,8,16},
					{2,2,2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,16},
					{4,4,4,4,4,4,4,8,8,8,8,8,8,16},
					{4,4,4,4,4,4,4,8,8,8,8,8,8,8,16},
					{4,4,8,8,8,8,8,8,16},
					{4,4,8,8,8,8,8,8,8,16,16,16,16,16,16,32},
					{8,8,16,16,16,16,16,32},
					//71-80
					{2,2,2,2,4,4,4,4,4,4,8,8,8,8,16},
					{4,4,4,4,8,8,8,8,8,8,16},
					{8,8,8,8,8,16},
					{4,4,4,4,4,8,8,8,8,16},
					{1,1,2,4},
					{4},
					{2,2,2,4},
					{4},
					{2,4,8},
					{4,8},
					//81-90
					{1,1,1,1,2,2,2,4},
					{2,2,2,2,4,4,8},
					{1,1,1,1,2,2,2,2,4,4,4,8},
					{2,2,2,2,2,2,4,4,4,4,8},
					{2,2,2,4,4,4,8},
					{2,2,4,4,4,4,8},
					{2,2,4,4,4,8,8,8,16},
					{4,4,8,8,8,16},
					{1,1,1,1,2,2,2,2,4,4,4,4,4,4,4,8},
					{2,2,2,4,4,4,8},
					//91-100
					{4,4,4,8},
					{4,8},
					{2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,8},
					{2,2,4,4,4,4,8},
					{4,4,4,8},
					{4,8},
					{2,2,4,4,4,8,8,8,8,8,16},
					{4,4,8,8,8,16},
					{1,1,2,4,4,4,8},
					{2,2,4,8},
					//101-110
					{2,2,4,4,8},
					{2,4,4,8},
					{2,2,4,8},
					{2,4,8},
					{2,2,2,4,4,8},
					{4,4,8},
					{2,4,8,8,16},
					{4,4,8,16},
					{4,8,16},
					{8,16},
					//111-120
					{1,1,1,1,2,2,2,2,4,4,4,4,4,4,8},
					{2,2,2,2,2,2,4,4,4,4,4,4,4,8},
					{2,2,2,4,4,8},
					{2,2,4,4,8},
					{1,1,1,1,2,2,2,4,4,4,4,8},
					{2,2,2,2,4,4,4,4,4,8},
					{2,2,2,2,4,4,4,4,8},
					{2,2,2,2,4,4,4,4,8},
					{2,2,2,2,4,4,8,8,8,16},
					{4,4,4,4,8,8,8,8,16},
					//121-130
					{2,2,4,4,4,8,8,8,8,16},
					{4,4,8,8,16},
					{1,1,1,1,2,2,2,2,4,4,4,4,4,4,4,8,8,8,8,8,16},
					{2,2,2,2,4,4,4,4,8,8,8,8,8,16},
					{2,2,2,2,4,4,4,4,8,8,8,8,8,16},
					{2,2,4,4,4,8,8,8,8,8,16},
					{2,2,2,2,4,4,4,4,8,8,8,16},
					{2,2,4,4,4,8,8,8,16},
					{2,2,2,4,4,4,8,8,8,8,16},
					{4,4,4,8,8,8,16},
					//131-140
					{2,2,2,2,2,2,4,4,4,4,4,4,4,8,8,8,8,16},
					{2,2,2,2,4,4,4,4,4,4,8,8,8,8,8,16},
					{4,4,4,4,8,8,8,8,8,8,16},
					{2,2,4,4,4,4,4,8,8,8,8,8,8,16},
					{4,4,4,4,8,8,8,8,16},
					{2,2,4,4,4,4,4,8,8,8,16},
					{2,2,4,4,8,8,8,16},
					{4,4,4,4,4,8,8,8,8,16},
					{2,2,4,4,4,8,8,8,8,8,16,16,16,16,32},
					{4,4,4,4,8,8,8,8,16,16,16,16,32},
					//141-150
					{4,4,8,8,8,16,16,16,32},
					{8,8,16,16,16,16,32},
					{1,1,1,3},
					{3},
					{3},
					{3,9},
					{1,1,2,2,3,3,6},
					{3,3,6,9,9,18},
					{1,1,1,1,1,1,2,2,2,3,3,6},
					{1,1,2,2,3,3,6},
					//151-160
					{3,3,6},
					{3,3,6},
					{3,3,6},
					{3,3,6},
					{3,3,6,9,9,18},
					{1,1,1,3,6},
					{1,2,3,6},
					{2,2,2,6},
					{2,2,6},
					{3,9,18},
					//161-170
					{6,18},
					{1,1,2,2,2,3,3,4,6,6,6,12},
					{2,2,2,2,4,4,6,6,12},
					{1,1,2,2,3,3,6,6,6,12},
					{2,2,4,4,6,6,12},
					{3,3,6,9,9,18,18,18,36},
					{6,6,12,18,18,36},
					{1,2,3,6},
					{6},
					{6},
					//171-180
					{3,3,6},
					{3,3,6},
					{2,2,6},
					{1,1,1,1,1,1,2,2,2,3,3,6},
					{1,1,2,2,2,3,3,4,6,6,6,12},
					{2,2,2,2,4,4,6,6,12},
					{1,1,2,2,2,3,3,4,6,6,6,6,6,12},
					{6,6,12},
					{6,6,12},
					{3,3,3,3,6,6,6,6,6,6,12},
					//181-190
					{3,3,3,3,6,6,6,6,6,6,12},
					{2,2,2,2,4,4,6,6,12},
					{1,2,3,6,6,12},
					{2,4,6,12},
					{2,4,6,12},
					{2,2,6,12},
					{1,1,1,1,1,1,2,2,2,3,3,6,6,6,12},
					{2,2,2,2,2,2,4,4,4,6,6,12},
					{1,1,2,2,2,3,3,4,6,6,6,12},
					{2,2,2,2,4,4,6,6,12},
					//191-200
					{1,1,2,2,2,3,3,4,6,6,6,6,6,12,12,12,12,24},
					{2,2,4,4,4,6,6,8,12,12,12,12,24},
					{2,2,4,4,4,6,6,8,12,12,12,24},
					{2,2,2,2,4,4,6,6,12,12,12,24},
					{1,1,3,3,4,6,6,6,6,12},
					{4,4,4,4,16,24,24,48},
					{2,6,8,12,12,24},
					{4,12},
					{8,12,24},
					{1,1,3,3,6,6,6,6,8,12,12,24},
					//201-210
					{2,4,4,6,8,12,12,24},
					{4,4,8,24,24,32,48,48,96},
					{8,8,16,32,48},
					{2,6,8,12,12,16,24},
					{4,4,8,24},
					{8,8,16,24,48},
					{1,1,3,3,6,6,8,12,12,12,24},
					{2,4,4,6,6,6,8,12,12,12,12,12,24},
					{4,4,8,24,24,32,48,48,48,96},
					{8,8,16,16,32,48,48,96},
					//211-220
					{2,6,8,12,12,16,24,24,24,48},
					{4,4,8,12,24},
					{4,4,8,12,24},
					{8,8,12,12,16,24,24,24,48},
					{1,1,3,3,4,6,6,12,12,24},
					{4,4,4,4,16,24,24,48,96},
					{2,6,8,12,12,24,24,48},
					{2,6,6,6,8,12,12,12,24},
					{8,8,24,24,32,48,48,96},
					{12,12,16,24,48},
					//221-230
					{1,1,3,3,6,6,8,12,12,12,24,24,24,48},
					{2,6,8,12,12,16,24,24,48},
					{2,6,6,6,8,12,12,12,16,24,24,48},
					{2,4,4,6,8,12,12,24,24,24,24,48},
					{4,4,8,24,24,32,48,48,48,96,96,192},
					{8,8,24,24,48,48,64,96,96,192},
					{8,8,16,16,32,48,96,96,192},
					{16,32,32,48,64,96,96,192},
					{2,6,8,12,12,16,24,24,48,48,48,96},
					{16,16,24,24,32,48,48,96},
					// Rhombohedral pseudo-groups (231-237)
					{1,3},
					{1,1,2,3,3,6},
					{1,1,2,3,3,6},
					{1,3,6},
					{2,6},
					{1,1,2,3,3,6,6,6,12},
					{2,2,4,6,6,12}
					};
			return multiplicities[spaceGroup];
		}
	}
	
	private static final String[] names = {
		"-",
		"P 1", // Triclinic 1-2
		"P 1̅",
		"P 1 2 1", // Monoclinic 3-15
		"P 1 2₁ 1",
		"C 1 2 1",
		"P 1 m 1",
		"P 1 c 1",
		"C 1 m 1",
		"C 1 c 1",
		"P 1 2/m 1",
		"P 1 2₁/m 1",
		"C 1 2/m 1",
		"P 1 2/c 1",
		"P 1 2₁/c 1",
		"C 1 2/c 1",
		"P 2 2 2", // Orthorhombic 16-74
		"P 2 2 2₁",
		"P 2₁ 2₁ 2",
		"P 2₁ 2₁ 2₁",
		"C 2 2 2₁",
		"C 2 2 2",
		"F 2 2 2",
		"I 2 2 2",
		"I 2₁ 2₁ 2₁",
		"P m m 2",
		"P m c 2₁",
		"P c c 2",
		"P m a 2",
		"P c a 2₁",
		"P n c 2",
		"P m n 2₁",
		"P b a 2",
		"P n a 2₁",
		"P n n 2",
		"C m m 2",
		"C m c 2₁",
		"C c c 2",
		"A m m 2",
		"A b m 2",
		"A m a 2",
		"A b a 2",
		"F m m 2",
		"F d d 2",
		"I m m 2",
		"I b a 2",
		"I m a 2",
		"P 2/m 2/m 2/m",
		"P 2/n 2/n 2/n",
		"P 2/c 2/c 2/m",
		"P 2/b 2/a 2/n",
		"P 2₁/m 2/m 2/a",
		"P 2/n 2₁/n 2/a",
		"P 2/m 2/n 2₁/a",
		"P 2₁/c 2/c 2/a",
		"P 2₁/b 2₁/a 2/m",
		"P 2₁/c 2₁/c 2/n",
		"P 2/b 2₁/c 2₁/m",
		"P 2₁/n 2₁/n 2/m",
		"P 2₁/m 2₁/m 2/n",
		"P 2₁/b 2/c 2₁/n",
		"P 2₁/b 2₁/c 2₁/a",
		"P 2₁/n 2₁/m 2₁/a",
		"C 2/m 2/c 2₁/m",
		"C 2/m 2/c 2₁/a",
		"C 2/m 2/m 2/m",
		"C 2/c 2/c 2/m",
		"C 2/m 2/m 2/e",
		"C 2/c 2/c 2/e",
		"F 2/m 2/m 2/m",
		"F 2/d 2/d 2/d",
		"I 2/m 2/m 2/m",
		"I 2/b 2/a 2/m",
		"I 2/b 2/c 2/a",
		"I 2/m, 2/m 2/a",
		"P 4", // Tetragonal 75-142
		"P 4₁",
		"P 4₂",
		"P 4₃",
		"I 4",
		"I 4₁",
		"P 4̅",
		"I 4̅",
		"P 4/m",
		"P 4₂/m",
		"P 4/n",
		"P 4₂/n",
		"I 4/m",
		"I 4₁/a",
		"P 4 2 2",
		"P 4 2₁ 2",
		"P 4₁ 2 2",
		"P 4₁ 2₁ 2",
		"P 4₂ 2 2",
		"P 4₂ 2₁ 2",
		"P 4₃ 2 2",
		"P 4₃ 2₁ 2",
		"I 4 2 2",
		"I 4₁ 2 2",
		"P 4 m m",
		"P 4 b m",
		"P 4₂ c m",
		"P 4₂ n m",
		"P 4 c c",
		"P 4 n c",
		"P 4₂ m c",
		"P 4₂ b c",
		"I 4 m m",
		"I 4 c m",
		"I 4₁ m d",
		"I 4₁ c d",
		"P 4̅ 2 m",
		"P 4̅ 2 c",
		"P 4̅ 2₁ m",
		"P 4̅ 2₁ c",
		"P 4̅ m 2",
		"P 4̅ c 2",
		"P 4̅ b 2",
		"P 4̅ n 2",
		"I 4̅ m 2",
		"I 4̅ c 2",
		"I 4̅ 2 m",
		"I 4̅ 2 d",
		"P 4/m 2/m 2/m",
		"P 4/m 2/c 2/c",
		"P 4/n 2/b 2/m",
		"P 4/n 2/n 2/c",
		"P 4/m 2₁/b 2/m",
		"P 4/m 2₁/n 2/c",
		"P 4/n 2₁/m 2/m",
		"P 4/n 2₁/c 2/c",
		"P 4₂/m 2/m 2/c",
		"P 4₂/m 2/c 2/m",
		"P 4₂/m 2/b 2/c",
		"P 4₂/n 2/n 2/m",
		"P 4₂/m 2₁/b 2/c",
		"P 4₂/m 2₁/n 2/m",
		"P 4₂/n 2₁/m 2/c",
		"P 4₂/n 2₁/c 2/m",
		"I 4/m 2/m 2/m",
		"I 4/m 2/c 2/m",
		"I 4₁/a 2/m 2/d",
		"I 4₁/a 2/c 2/d",
		"P 3", // Trigonal 143-167
		"P 3₁",
		"P 3₂",
		"R 3",
		"P 3̅",
		"R 3̅",
		"P 3 1 2",
		"P 3 2 1",
		"P 3₁ 1 2",
		"P 3₁ 2 1",
		"P 3₂ 1 2",
		"P 3₂ 2 1",
		"R 3 2",
		"P 3 m 1",
		"P 3 1 m",
		"P 3 c 1",
		"P 3 1 c",
		"R 3 m",
		"R c 3",
		"P 3̅ 1 2/m",
		"P 3̅ 1 2/c",
		"P 3̅ 2/m 1",
		"P 3̅ 2/c 1",
		"R 3̅ 2/m",
		"R 3̅ 2/c",
		"P 6", // Hexagonal 168-194
		"P 6₁",
		"P 6₅",
		"P 6₂",
		"P 6₄",
		"P 6₃",
		"P 6̅",
		"P 6/m",
		"P 6₃/m",
		"P 6 2 2",
		"P 6₁ 2 2",
		"P 6₅ 2 2",
		"P 6₂ 2 2",
		"P 6₄ 2 2",
		"P 6₃ 2 2",
		"P 6 m m",
		"P 6 c c",
		"P 6₃ c m",
		"P 6₃ m c",
		"P 6̅ m 2",
		"P 6̅ c 2",
		"P 6̅ 2 m",
		"P 6̅ 2 c",
		"P 6/m 2/m 2/m",
		"P 6/m 2/c 2/c",
		"P 6₃/m 2/c 2/m",
		"P 6₃/m 2/m 2/c",
		"P 2 3", // Cubic 195-230
		"F 2 3",
		"I 2 3",
		"P 2₁ 3",
		"I 2₁ 3",
		"P 2/m 3̅",
		"P 2/n 3̅",
		"F 2/m 3̅",
		"F 2/d 3̅",
		"I 2/m 3̅",
		"P 2₁/a 3̅",
		"I 2₁/a 3̅",
		"P 4 3 2",
		"P 4₂ 3 2",
		"F 4 3 2",
		"F 4₁ 3 2",
		"I 4 3 2",
		"P 4₃ 3 2",
		"P 4₁ 3 2",
		"I 4₁ 3 2",
		"P 4̅ 3 m",
		"F 4̅ 3 m",
		"I 4̅ 3 m",
		"P 4̅ 3 n",
		"F 4̅ 3 c",
		"I 4̅ 3 d",
		"P 4/m 3̅ 2/m",
		"P 4/n 3̅ 2/n",
		"P 4₂/m 3̅ 2/n",
		"P 4₂/n 3̅ 2/m",
		"F 4/m 3̅ 2/m",
		"F 4/m 3̅ 2/c",
		"F 4₁/d 3̅ 2/m",
		"F 4₁/d 3̅ 2/c",
		"I 4/m 3̅ 2/m",
		"I 4₁/a 3̅ 2/d",
		// Trigonal, rhombohedral basis 146, 148, 155, 160, 161, 166, 167
		"R 3:R",
		"R 3̅:R",
		"R 3 2:R",
		"R 3 m:R",
		"R c 3:R",
		"R 3̅ 2/m:R",
		"R 3̅ 2/c:R"
	};

	private static final String[] shortNames = {
		"-",
		"P1", 
		"P-1",
		"P2",
		"P21",
		"C2",
		"Pm",
		"Pc",
		"Cm",
		"Cc",
		"P2/m",
		"P21/m",
		"C2/m",
		"P2/c",
		"P21/c",
		"C2/c",
		"P222",
		"P2221",
		"P21212",
		"P212121",
		"C2221",
		"C222",
		"F222",
		"I222",
		"I212121",
		"Pmm2",
		"Pmc21",
		"Pcc2",
		"Pma2",
		"Pca21",
		"Pnc2",
		"Pmn21",
		"Pba2",
		"Pna21",
		"Pnn2",
		"Cmm2",
		"Cmc21",
		"Ccc2",
		"Amm2",
		"Abm2",
		"Ama2",
		"Aba2",
		"Fmm2",
		"Fdd2",
		"Imm2",
		"Iba2",
		"Ima2",
		"Pmmm",
		"Pnnn",
		"Pccm",
		"Pban",
		"Pmma",
		"Pnna",
		"Pmna",
		"Pcca",
		"Pbam",
		"Pccn",
		"Pbcm",
		"Pnnm",
		"Pmmn",
		"Pbcn",
		"Pbca",
		"Pnma",
		"Cmcm",
		"Cmca",
		"Cmmm",
		"Cccm",
		"Cmme",
		"Ccce",
		"Fmmm",
		"Fddd",
		"Immm",
		"Ibam",
		"Ibca",
		"Imma",
		"P4",
		"P41",
		"P42",
		"P43",
		"I4",
		"I41",
		"P-4",
		"I-4",
		"P4/m",
		"P42/m",
		"P4/n",
		"P42/n",
		"I4/m",
		"I41/a",
		"P422",
		"P4212",
		"P4122",
		"P41212",
		"P4222",
		"P42212",
		"P4322",
		"P43212",
		"I422",
		"I4122",
		"P4mm",
		"P4bm",
		"P42cm",
		"P42nm",
		"P4cc",
		"P4nc",
		"P42mc",
		"P42bc",
		"I4mm",
		"I4cm",
		"I41md",
		"I41cd",
		"P-42m",
		"P-42c",
		"P-421m",
		"P-421c",
		"P-4m2",
		"P-4c2",
		"P-4b2",
		"P-4n2",
		"I-4m2",
		"I-4c2",
		"I-42m",
		"I-42d",
		"P4/mmm",
		"P4/mcc",
		"P4/nbm",
		"P4/nnc",
		"P4/mbm",
		"P4/mnc",
		"P4/nmm",
		"P4/ncc",
		"P42/mmc",
		"P42/mcm",
		"P42/nbc",
		"P42/nnm",
		"P42/mbc",
		"P42/mnm",
		"P42/nmc",
		"P42/ncm",
		"I4/mmm",
		"I4/mcm",
		"I41/amd",
		"I41/acd",
		"P3",
		"P31",
		"P32",
		"R3",
		"P-3",
		"R-3",
		"P312",
		"P321",
		"P3112",
		"P3121",
		"P3212",
		"P3221",
		"R32",
		"P3m1",
		"P31m",
		"P3c1",
		"P31c",
		"R3m",
		"R3c",
		"P-31m",
		"P-31c",
		"P-3m1",
		"P-3c1",
		"R-3m",
		"R-3c",
		"P6",
		"P61",
		"P65",
		"P62",
		"P64",
		"P63",
		"P-6",
		"P6/m",
		"P63/m",
		"P622",
		"P6122",
		"P6522",
		"P6222",
		"P6422",
		"P6322",
		"P6mm",
		"P6cc",
		"P63cm",
		"P63mc",
		"P-6m2",
		"P-6c2",
		"P-62m",
		"P-62c",
		"P6/mmm",
		"P6/mcc",
		"P63/mcm",
		"P63/mmc",
		"P23",
		"F23",
		"I23",
		"P213",
		"I213",
		"Pm-3",
		"Pn-3",
		"Fm-3",
		"Fd-3",
		"Im-3",
		"Pa-3",
		"Ia-3",
		"P432",
		"P4232",
		"F432",
		"F4132",
		"I432",
		"P4332",
		"P4132",
		"I4132",
		"P-43m",
		"F-43m",
		"I-43m",
		"P-43n",
		"F-43c",
		"I-43d",
		"Pm-3m",
		"Pn-3n",
		"Pm-3n",
		"Pn-3m",
		"Fm-3m",
		"Fm-3c",
		"Fd-3m",
		"Fd-3c",
		"Im-3m",
		"Ia-3d",
		"R3:R",
		"R-3:R",
		"R32:R",
		"R3m:R",
		"R3c:R",
		"R-3m:R",
		"R-3c:R",

	};

	private static String[][] allSymOps = {
			{"x,y,z"}, // the non-group still has the identity, I guess
			{"x,y,z"},
			{"x,y,z", "-x,-y,-z"},
			{"x,y,z", "-x,y,-z"},
			{"x,y,z", "-x,y+1/2,-z"},
			{"x,y,z", "-x,y,-z", "x+1/2,y+1/2,z", "-x+1/2,y+1/2,-z"},
			{"x,y,z", "x,-y,z"},
			{"x,y,z", "x,-y,z+1/2"},
			{"x,y,z", "x,-y,z", "x+1/2,y+1/2,z", "x+1/2,-y+1/2,z"},
			{"x,y,z", "x,-y,z+1/2", "x+1/2,y+1/2,z", "x+1/2,-y+1/2,z+1/2"},
			{"x,y,z", "-x,y,-z", "-x,-y,-z", "x,-y,z"},
			{"x,y,z", "-x,y+1/2,-z", "-x,-y,-z", "x,-y+1/2,z"},
			{"x,y,z", "-x,y,-z", "-x,-y,-z", "x,-y,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"},
			{"x,y,z", "-x,y,-z+1/2", "-x,-y,-z", "x,-y,z+1/2"},
			{"x,y,z", "-x,y+1/2,-z+1/2", "-x,-y,-z", "x,-y+1/2,z+1/2"},
			{"x,y,z", "-x,y,-z+1/2", "-x,-y,-z", "x,-y,z+1/2", "x+1/2,y+1/2,z", "-x+1/2,y+1/2,-z+1/2", "-x+1/2,-y+1/2,-z", "x+1/2,-y+1/2,z+1/2"},
			{"x,y,z", "-x,-y,z", "-x,y,-z", "x,-y,-z"},
			{"x,y,z", "-x,-y,z+1/2", "-x,y,-z+1/2", "x,-y,-z"},
			{"x,y,z", "-x,-y,z", "-x+1/2,y+1/2,-z", "x+1/2,-y+1/2,-z"},
			{"x,y,z", "-x+1/2,-y,z+1/2", "-x,y+1/2,-z+1/2", "x+1/2,-y+1/2,-z"},
			{"x,y,z", "-x,-y,z+1/2", "-x,y,-z+1/2", "x,-y,-z", "x+1/2,y+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,y,z", "-x,-y,z", "-x,y,-z", "x,-y,-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"},
			{"x,y,z", "-x,-y,z", "-x,y,-z", "x,-y,-z", "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", "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", "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"},
			{"x,y,z", "-x,-y,z", "-x,y,-z", "x,-y,-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+1/2", "x+1/2,-y+1/2,-z+1/2"},
			{"x,y,z", "-x+1/2,-y,z+1/2", "-x,y+1/2,-z+1/2", "x+1/2,-y+1/2,-z", "x+1/2,y+1/2,z+1/2", "-x,-y+1/2,z", "-x+1/2,y,-z", "x,-y,-z+1/2"},
			{"x,y,z", "-x,-y,z", "x,-y,z", "-x,y,z"},
			{"x,y,z", "-x,-y,z+1/2", "x,-y,z+1/2", "-x,y,z"},
			{"x,y,z", "-x,-y,z", "x,-y,z+1/2", "-x,y,z+1/2"},
			{"x,y,z", "-x,-y,z", "x+1/2,-y,z", "-x+1/2,y,z"},
			{"x,y,z", "-x,-y,z+1/2", "x+1/2,-y,z", "-x+1/2,y,z+1/2"},
			{"x,y,z", "-x,-y,z", "x,-y+1/2,z+1/2", "-x,y+1/2,z+1/2"},
			{"x,y,z", "-x+1/2,-y,z+1/2", "x+1/2,-y,z+1/2", "-x,y,z"},
			{"x,y,z", "-x,-y,z", "x+1/2,-y+1/2,z", "-x+1/2,y+1/2,z"},
			{"x,y,z", "-x,-y,z+1/2", "x+1/2,-y+1/2,z", "-x+1/2,y+1/2,z+1/2"},
			{"x,y,z", "-x,-y,z", "x+1/2,-y+1/2,z+1/2", "-x+1/2,y+1/2,z+1/2"},
			{"x,y,z", "-x,-y,z", "x,-y,z", "-x,y,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"},
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			{"x,y,z", "-x+1/4,-y+3/4,z+1/2", "-x+3/4,y+1/2,-z+1/4", "x+1/2,-y+1/4,-z+3/4", "z,x,y", "z+1/2,-x+1/4,-y+3/4", "-z+1/4,-x+3/4,y+1/2", "-z+3/4,x+1/2,-y+1/4", "y,z,x", "-y+3/4,z+1/2,-x+1/4", "y+1/2,-z+1/4,-x+3/4", "-y+1/4,-z+3/4,x+1/2", "y+3/4,x+1/4,-z", "-y+1/2,-x+1/2,-z+1/2", "y+1/4,-x,z+3/4", "-y,x+3/4,z+1/4", "x+3/4,z+1/4,-y", "-x,z+3/4,y+1/4", "-x+1/2,-z+1/2,-y+1/2", "x+1/4,-z,y+3/4", "z+3/4,y+1/4,-x", "z+1/4,-y,x+3/4", "-z,y+3/4,x+1/4", "-z+1/2,-y+1/2,-x+1/2", "-x,-y,-z", "x+3/4,y+1/4,-z+1/2", "x+1/4,-y+1/2,z+3/4", "-x+1/2,y+3/4,z+1/4", "-z,-x,-y", "-z+1/2,x+3/4,y+1/4", "z+3/4,x+1/4,-y+1/2", "z+1/4,-x+1/2,y+3/4", "-y,-z,-x", "y+1/4,-z+1/2,x+3/4", "-y+1/2,z+3/4,x+1/4", "y+3/4,z+1/4,-x+1/2", "-y+1/4,-x+3/4,z", "y+1/2,x+1/2,z+1/2", "-y+3/4,x,-z+1/4", "y,-x+1/4,-z+3/4", "-x+1/4,-z+3/4,y", "x,-z+1/4,-y+3/4", "x+1/2,z+1/2,y+1/2", "-x+3/4,z,-y+1/4", "-z+1/4,-y+3/4,x", "-z+3/4,y,-x+1/4", "z,-y+1/4,-x+3/4", "z+1/2,y+1/2,x+1/2", "x,y+1/2,z+1/2", "-x+1/4,-y+1/4,z", "-x+3/4,y,-z+3/4", "x+1/2,-y+3/4,-z+1/4", "z,x+1/2,y+1/2", "z+1/2,-x+3/4,-y+1/4", "-z+1/4,-x+1/4,y", "-z+3/4,x,-y+3/4", "y,z+1/2,x+1/2", "-y+3/4,z,-x+3/4", "y+1/2,-z+3/4,-x+1/4", "-y+1/4,-z+1/4,x", "y+3/4,x+3/4,-z+1/2", "-y+1/2,-x,-z", "y+1/4,-x+1/2,z+1/4", "-y,x+1/4,z+3/4", "x+3/4,z+3/4,-y+1/2", "-x,z+1/4,y+3/4", "-x+1/2,-z,-y", "x+1/4,-z+1/2,y+1/4", "z+3/4,y+3/4,-x+1/2", "z+1/4,-y+1/2,x+1/4", "-z,y+1/4,x+3/4", "-z+1/2,-y,-x", "-x,-y+1/2,-z+1/2", "x+3/4,y+3/4,-z", "x+1/4,-y,z+1/4", "-x+1/2,y+1/4,z+3/4", "-z,-x+1/2,-y+1/2", "-z+1/2,x+1/4,y+3/4", "z+3/4,x+3/4,-y", "z+1/4,-x,y+1/4", "-y,-z+1/2,-x+1/2", "y+1/4,-z,x+1/4", "-y+1/2,z+1/4,x+3/4", "y+3/4,z+3/4,-x", "-y+1/4,-x+1/4,z+1/2", "y+1/2,x,z", "-y+3/4,x+1/2,-z+3/4", "y,-x+3/4,-z+1/4", "-x+1/4,-z+1/4,y+1/2", "x,-z+3/4,-y+1/4", "x+1/2,z,y", "-x+3/4,z+1/2,-y+3/4", "-z+1/4,-y+1/4,x+1/2", "-z+3/4,y+1/2,-x+3/4", "z,-y+3/4,-x+1/4", "z+1/2,y,x", "x+1/2,y,z+1/2", "-x+3/4,-y+3/4,z", "-x+1/4,y+1/2,-z+3/4", "x,-y+1/4,-z+1/4", "z+1/2,x,y+1/2", "z,-x+1/4,-y+1/4", "-z+3/4,-x+3/4,y", "-z+1/4,x+1/2,-y+3/4", "y+1/2,z,x+1/2", "-y+1/4,z+1/2,-x+3/4", "y,-z+1/4,-x+1/4", "-y+3/4,-z+3/4,x", "y+1/4,x+1/4,-z+1/2", "-y,-x+1/2,-z", "y+3/4,-x,z+1/4", "-y+1/2,x+3/4,z+3/4", "x+1/4,z+1/4,-y+1/2", "-x+1/2,z+3/4,y+3/4", "-x,-z+1/2,-y", "x+3/4,-z,y+1/4", "z+1/4,y+1/4,-x+1/2", "z+3/4,-y,x+1/4", "-z+1/2,y+3/4,x+3/4", "-z,-y+1/2,-x", "-x+1/2,-y,-z+1/2", "x+1/4,y+1/4,-z", "x+3/4,-y+1/2,z+1/4", "-x,y+3/4,z+3/4", "-z+1/2,-x,-y+1/2", "-z,x+3/4,y+3/4", "z+1/4,x+1/4,-y", "z+3/4,-x+1/2,y+1/4", "-y+1/2,-z,-x+1/2", "y+3/4,-z+1/2,x+1/4", "-y,z+3/4,x+3/4", "y+1/4,z+1/4,-x", "-y+3/4,-x+3/4,z+1/2", "y,x+1/2,z", "-y+1/4,x,-z+3/4", "y+1/2,-x+1/4,-z+1/4", "-x+3/4,-z+3/4,y+1/2", "x+1/2,-z+1/4,-y+1/4", "x,z+1/2,y", "-x+1/4,z,-y+3/4", "-z+3/4,-y+3/4,x+1/2", "-z+1/4,y,-x+3/4", "z+1/2,-y+1/4,-x+1/4", "z,y+1/2,x", "x+1/2,y+1/2,z", "-x+3/4,-y+1/4,z+1/2", "-x+1/4,y,-z+1/4", "x,-y+3/4,-z+3/4", "z+1/2,x+1/2,y", "z,-x+3/4,-y+3/4", "-z+3/4,-x+1/4,y+1/2", "-z+1/4,x,-y+1/4", "y+1/2,z+1/2,x", "-y+1/4,z,-x+1/4", "y,-z+3/4,-x+3/4", "-y+3/4,-z+1/4,x+1/2", "y+1/4,x+3/4,-z", "-y,-x,-z+1/2", "y+3/4,-x+1/2,z+3/4", "-y+1/2,x+1/4,z+1/4", "x+1/4,z+3/4,-y", "-x+1/2,z+1/4,y+1/4", "-x,-z,-y+1/2", "x+3/4,-z+1/2,y+3/4", "z+1/4,y+3/4,-x", "z+3/4,-y+1/2,x+3/4", "-z+1/2,y+1/4,x+1/4", "-z,-y,-x+1/2", "-x+1/2,-y+1/2,-z", "x+1/4,y+3/4,-z+1/2", "x+3/4,-y,z+3/4", "-x,y+1/4,z+1/4", "-z+1/2,-x+1/2,-y", "-z,x+1/4,y+1/4", "z+1/4,x+3/4,-y+1/2", "z+3/4,-x,y+3/4", "-y+1/2,-z+1/2,-x", "y+3/4,-z,x+3/4", "-y,z+1/4,x+1/4", "y+1/4,z+3/4,-x+1/2", "-y+3/4,-x+1/4,z", "y,x,z+1/2", "-y+1/4,x+1/2,-z+1/4", "y+1/2,-x+3/4,-z+3/4", "-x+3/4,-z+1/4,y", "x+1/2,-z+3/4,-y+3/4", "x,z,y+1/2", "-x+1/4,z+1/2,-y+1/4", "-z+3/4,-y+1/4,x", "-z+1/4,y+1/2,-x+1/4", "z+1/2,-y+3/4,-x+3/4", "z,y,x+1/2"},
			{"x,y,z", "-x,-y,z", "-x,y,-z", "x,-y,-z", "z,x,y", "z,-x,-y", "-z,-x,y", "-z,x,-y", "y,z,x", "-y,z,-x", "y,-z,-x", "-y,-z,x", "y,x,-z", "-y,-x,-z", "y,-x,z", "-y,x,z", "x,z,-y", "-x,z,y", "-x,-z,-y", "x,-z,y", "z,y,-x", "z,-y,x", "-z,y,x", "-z,-y,-x", "-x,-y,-z", "x,y,-z", "x,-y,z", "-x,y,z", "-z,-x,-y", "-z,x,y", "z,x,-y", "z,-x,y", "-y,-z,-x", "y,-z,x", "-y,z,x", "y,z,-x", "-y,-x,z", "y,x,z", "-y,x,-z", "y,-x,-z", "-x,-z,y", "x,-z,-y", "x,z,y", "-x,z,-y", "-z,-y,x", "-z,y,-x", "z,-y,-x", "z,y,x", "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+1/2", "x+1/2,-y+1/2,-z+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+1/2,x+1/2,-y+1/2", "y+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+1/2,x+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", "-y+1/2,x+1/2,z+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,y+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,-y+1/2,-x+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+1/2", "-x+1/2,y+1/2,z+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+1/2,-x+1/2,y+1/2", "-y+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+1/2,-x+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", "y+1/2,-x+1/2,-z+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,-y+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,y+1/2,x+1/2"},
			{"x,y,z", "-x+1/2,-y,z+1/2", "-x,y+1/2,-z+1/2", "x+1/2,-y+1/2,-z", "z,x,y", "z+1/2,-x+1/2,-y", "-z+1/2,-x,y+1/2", "-z,x+1/2,-y+1/2", "y,z,x", "-y,z+1/2,-x+1/2", "y+1/2,-z+1/2,-x", "-y+1/2,-z,x+1/2", "y+3/4,x+1/4,-z+1/4", "-y+3/4,-x+3/4,-z+3/4", "y+1/4,-x+1/4,z+3/4", "-y+1/4,x+3/4,z+1/4", "x+3/4,z+1/4,-y+1/4", "-x+1/4,z+3/4,y+1/4", "-x+3/4,-z+3/4,-y+3/4", "x+1/4,-z+1/4,y+3/4", "z+3/4,y+1/4,-x+1/4", "z+1/4,-y+1/4,x+3/4", "-z+1/4,y+3/4,x+1/4", "-z+3/4,-y+3/4,-x+3/4", "-x,-y,-z", "x+1/2,y,-z+1/2", "x,-y+1/2,z+1/2", "-x+1/2,y+1/2,z", "-z,-x,-y", "-z+1/2,x+1/2,y", "z+1/2,x,-y+1/2", "z,-x+1/2,y+1/2", "-y,-z,-x", "y,-z+1/2,x+1/2", "-y+1/2,z+1/2,x", "y+1/2,z,-x+1/2", "-y+1/4,-x+3/4,z+3/4", "y+1/4,x+1/4,z+1/4", "-y+3/4,x+3/4,-z+1/4", "y+3/4,-x+1/4,-z+3/4", "-x+1/4,-z+3/4,y+3/4", "x+3/4,-z+1/4,-y+3/4", "x+1/4,z+1/4,y+1/4", "-x+3/4,z+3/4,-y+1/4", "-z+1/4,-y+3/4,x+3/4", "-z+3/4,y+3/4,-x+1/4", "z+3/4,-y+1/4,-x+3/4", "z+1/4,y+1/4,x+1/4", "x+1/2,y+1/2,z+1/2", "-x,-y+1/2,z", "-x+1/2,y,-z", "x,-y,-z+1/2", "z+1/2,x+1/2,y+1/2", "z,-x,-y+1/2", "-z,-x+1/2,y", "-z+1/2,x,-y", "y+1/2,z+1/2,x+1/2", "-y+1/2,z,-x", "y,-z,-x+1/2", "-y,-z+1/2,x", "y+1/4,x+3/4,-z+3/4", "-y+1/4,-x+1/4,-z+1/4", "y+3/4,-x+3/4,z+1/4", "-y+3/4,x+1/4,z+3/4", "x+1/4,z+3/4,-y+3/4", "-x+3/4,z+1/4,y+3/4", "-x+1/4,-z+1/4,-y+1/4", "x+3/4,-z+3/4,y+1/4", "z+1/4,y+3/4,-x+3/4", "z+3/4,-y+3/4,x+1/4", "-z+3/4,y+1/4,x+3/4", "-z+1/4,-y+1/4,-x+1/4", "-x+1/2,-y+1/2,-z+1/2", "x,y+1/2,-z", "x+1/2,-y,z", "-x,y,z+1/2", "-z+1/2,-x+1/2,-y+1/2", "-z,x,y+1/2", "z,x+1/2,-y", "z+1/2,-x,y", "-y+1/2,-z+1/2,-x+1/2", "y+1/2,-z,x", "-y,z,x+1/2", "y,z+1/2,-x", "-y+3/4,-x+1/4,z+1/4", "y+3/4,x+3/4,z+3/4", "-y+1/4,x+1/4,-z+3/4", "y+1/4,-x+3/4,-z+1/4", "-x+3/4,-z+1/4,y+1/4", "x+1/4,-z+3/4,-y+1/4", "x+3/4,z+3/4,y+3/4", "-x+1/4,z+1/4,-y+3/4", "-z+3/4,-y+1/4,x+1/4", "-z+1/4,y+1/4,-x+3/4", "z+1/4,-y+3/4,-x+1/4", "z+3/4,y+3/4,x+3/4"},
			{"x,y,z", "-y,x-y,z", "-x+y,-x,z", "x+2/3,y+1/3,z+1/3", "-y+2/3,x-y+1/3,z+1/3", "-x+y+2/3,-x+1/3,z+1/3", "x+1/3,y+2/3,z+2/3", "-y+1/3,x-y+2/3,z+2/3", "-x+y+1/3,-x+2/3,z+2/3"},
			{"x,y,z", "-y,x-y,z", "-x+y,-x,z", "-x,-y,-z", "y,-x+y,-z", "x-y,x,-z", "x+2/3,y+1/3,z+1/3", "-y+2/3,x-y+1/3,z+1/3", "-x+y+2/3,-x+1/3,z+1/3", "-x+2/3,-y+1/3,-z+1/3", "y+2/3,-x+y+1/3,-z+1/3", "x-y+2/3,x+1/3,-z+1/3", "x+1/3,y+2/3,z+2/3", "-y+1/3,x-y+2/3,z+2/3", "-x+y+1/3,-x+2/3,z+2/3", "-x+1/3,-y+2/3,-z+2/3", "y+1/3,-x+y+2/3,-z+2/3", "x-y+1/3,x+2/3,-z+2/3"},
			{"x,y,z", "-y,x-y,z", "-x+y,-x,z", "y,x,-z", "x-y,-y,-z", "-x,-x+y,-z", "x+2/3,y+1/3,z+1/3", "-y+2/3,x-y+1/3,z+1/3", "-x+y+2/3,-x+1/3,z+1/3", "y+2/3,x+1/3,-z+1/3", "x-y+2/3,-y+1/3,-z+1/3", "-x+2/3,-x+y+1/3,-z+1/3", "x+1/3,y+2/3,z+2/3", "-y+1/3,x-y+2/3,z+2/3", "-x+y+1/3,-x+2/3,z+2/3", "y+1/3,x+2/3,-z+2/3", "x-y+1/3,-y+2/3,-z+2/3", "-x+1/3,-x+y+2/3,-z+2/3"},
			{"x,y,z", "-y,x-y,z", "-x+y,-x,z", "-y,-x,z", "-x+y,y,z", "x,x-y,z", "x+2/3,y+1/3,z+1/3", "-y+2/3,x-y+1/3,z+1/3", "-x+y+2/3,-x+1/3,z+1/3", "-y+2/3,-x+1/3,z+1/3", "-x+y+2/3,y+1/3,z+1/3", "x+2/3,x-y+1/3,z+1/3", "x+1/3,y+2/3,z+2/3", "-y+1/3,x-y+2/3,z+2/3", "-x+y+1/3,-x+2/3,z+2/3", "-y+1/3,-x+2/3,z+2/3", "-x+y+1/3,y+2/3,z+2/3", "x+1/3,x-y+2/3,z+2/3"},
			{"x,y,z", "-y,x-y,z", "-x+y,-x,z", "-y,-x,z+1/2", "-x+y,y,z+1/2", "x,x-y,z+1/2", "x+2/3,y+1/3,z+1/3", "-y+2/3,x-y+1/3,z+1/3", "-x+y+2/3,-x+1/3,z+1/3", "-y+2/3,-x+1/3,z+5/6", "-x+y+2/3,y+1/3,z+5/6", "x+2/3,x-y+1/3,z+5/6", "x+1/3,y+2/3,z+2/3", "-y+1/3,x-y+2/3,z+2/3", "-x+y+1/3,-x+2/3,z+2/3", "-y+1/3,-x+2/3,z+1/6", "-x+y+1/3,y+2/3,z+1/6", "x+1/3,x-y+2/3,z+1/6"},
			{"x,y,z", "-y,x-y,z", "-x+y,-x,z", "y,x,-z+1/2", "x-y,-y,-z+1/2", "-x,-x+y,-z+1/2", "-x,-y,-z", "y,-x+y,-z", "x-y,x,-z", "-y,-x,z+1/2", "-x+y,y,z+1/2", "x,x-y,z+1/2", "x+2/3,y+1/3,z+1/3", "-y+2/3,x-y+1/3,z+1/3", "-x+y+2/3,-x+1/3,z+1/3", "y+2/3,x+1/3,-z+5/6", "x-y+2/3,-y+1/3,-z+5/6", "-x+2/3,-x+y+1/3,-z+5/6", "-x+2/3,-y+1/3,-z+1/3", "y+2/3,-x+y+1/3,-z+1/3", "x-y+2/3,x+1/3,-z+1/3", "-y+2/3,-x+1/3,z+5/6", "-x+y+2/3,y+1/3,z+5/6", "x+2/3,x-y+1/3,z+5/6", "x+1/3,y+2/3,z+2/3", "-y+1/3,x-y+2/3,z+2/3", "-x+y+1/3,-x+2/3,z+2/3", "y+1/3,x+2/3,-z+1/6", "x-y+1/3,-y+2/3,-z+1/6", "-x+1/3,-x+y+2/3,-z+1/6", "-x+1/3,-y+2/3,-z+2/3", "y+1/3,-x+y+2/3,-z+2/3", "x-y+1/3,x+2/3,-z+2/3", "-y+1/3,-x+2/3,z+1/6", "-x+y+1/3,y+2/3,z+1/6", "x+1/3,x-y+2/3,z+1/6"},
			{"x,y,z", "-y,x-y,z", "-x+y,-x,z", "-x,-y,z", "y,-x+y,z", "x-y,x,z"}
	};
	
	public static void main(String[] args) {
		String sg225hm = "F 4/m -3 2/m";
		System.out.println(sg225hm + "->" + Pattern.compile(" +").matcher(sg225hm).replaceAll(""));
		System.out.println(names[225] + "->" + simplifyLongName(names[225]));
		System.out.println(names[138] + "->" + simplifyLongName(names[138]));
		System.out.println(names[230] + "->" + simplifyLongName(names[230]));
		System.out.println(get("Fm3m").getNumber());
		
	}

	
	
}