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/**
* Copyright (c) 2018-2019 mol* contributors, licensed under MIT, See LICENSE file for more info.
*
* @author David Sehnal <david.sehnal@gmail.com>
* @author Alexander Rose <alexander.rose@weirdbyte.de>
*/
export const TransformData = [
[1.0, 0.0, 0.0, 0.0],
[0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, 1.0, 0.0],
[-1.0, 0.0, 0.0, 0.0],
[0.0, -1.0, 0.0, 0.0],
[0.0, 0.0, -1.0, 0.0],
[0.0, 1.0, 0.0, 0.5],
[1.0, 0.0, 0.0, 0.5],
[-1.0, 0.0, 0.0, 0.5],
[0.0, 0.0, 1.0, 0.5],
[0.0, -1.0, 0.0, 0.5],
[0.0, 0.0, -1.0, 0.5],
[1.0, 0.0, 0.0, 0.25],
[0.0, -1.0, 0.0, 0.25],
[0.0, 0.0, 1.0, 0.25],
[-1.0, 0.0, 0.0, 0.25],
[0.0, 1.0, 0.0, 0.25],
[0.0, -1.0, 0.0, 0.75],
[0.0, 0.0, 1.0, 0.75],
[0.0, 1.0, 0.0, 0.75],
[1.0, 0.0, 0.0, 0.75],
[-1.0, 0.0, 0.0, 0.75],
[0.0, 0.0, -1.0, 0.25],
[0.0, 0.0, -1.0, 0.75],
[1.0, -1.0, 0.0, 0.0],
[-1.0, 1.0, 0.0, 0.0],
[0.0, 0.0, 1.0, 1 / 3],
[0.0, 0.0, 1.0, 2 / 3],
[1.0, 0.0, 0.0, 2 / 3],
[0.0, 1.0, 0.0, 1 / 3],
[0.0, -1.0, 0.0, 2 / 3],
[1.0, -1.0, 0.0, 1 / 3],
[-1.0, 1.0, 0.0, 2 / 3],
[-1.0, 0.0, 0.0, 1 / 3],
[1.0, 0.0, 0.0, 1 / 3],
[0.0, 1.0, 0.0, 2 / 3],
[0.0, -1.0, 0.0, 1 / 3],
[1.0, -1.0, 0.0, 2 / 3],
[-1.0, 1.0, 0.0, 1 / 3],
[-1.0, 0.0, 0.0, 2 / 3],
[0.0, 0.0, -1.0, 1 / 3],
[0.0, 0.0, -1.0, 2 / 3],
[0.0, 0.0, 1.0, 5 / 6],
[0.0, 0.0, 1.0, 1 / 6],
[0.0, 0.0, -1.0, 5 / 6],
[0.0, 0.0, -1.0, 1 / 6],
];
export const OperatorData = [
[0, 1, 2],
[3, 4, 5],
[3, 1, 5],
[3, 6, 5],
[7, 6, 2],
[8, 6, 5],
[0, 4, 2],
[0, 4, 9],
[7, 10, 2],
[7, 10, 9],
[0, 10, 2],
[8, 10, 5],
[3, 1, 11], [3, 6, 11],
[0, 10, 9],
[8, 6, 11],
[3, 4, 2],
[0, 4, 5],
[3, 4, 9],
[7, 10, 5],
[8, 4, 9],
[8, 10, 9],
[8, 10, 2],
[0, 6, 9],
[3, 10, 9],
[0, 10, 11],
[7, 1, 9],
[8, 1, 11],
[7, 4, 11],
[7, 6, 9],
[7, 10, 11],
[3, 10, 2],
[8, 1, 5],
[0, 4, 11],
[3, 1, 2],
[3, 1, 9],
[7, 4, 2],
[8, 1, 2],
[8, 1, 9],
[3, 6, 9],
[7, 4, 9],
[8, 6, 2],
[8, 6, 9],
[3, 6, 2],
[12, 13, 14],
[15, 16, 14],
[12, 17, 18],
[15, 19, 18],
[20, 13, 18],
[21, 16, 18],
[20, 17, 14],
[21, 19, 14],
[0, 1, 5],
[8, 10, 11],
[7, 6, 11],
[7, 6, 5],
[8, 4, 2],
[7, 4, 5],
[7, 1, 5],
[7, 1, 11],
[0, 10, 5],
[0, 1, 11],
[0, 6, 11],
[0, 6, 5],
[3, 10, 11],
[8, 4, 11],
[15, 13, 22],
[12, 16, 22],
[15, 17, 23],
[12, 19, 23],
[21, 13, 23],
[20, 16, 23],
[21, 17, 22],
[20, 19, 22],
[4, 0, 2],
[1, 3, 2],
[4, 0, 14],
[1, 3, 18],
[4, 0, 9],
[1, 3, 9],
[4, 0, 18],
[1, 3, 14],
[10, 7, 9], [6, 8, 9],
[4, 7, 14],
[6, 3, 18],
[10, 0, 18],
[1, 8, 14],
[1, 3, 5],
[4, 0, 5],
[6, 8, 11],
[10, 7, 11],
[1, 3, 11],
[4, 0, 11],
[10, 7, 2],
[6, 8, 2],
[3, 10, 22],
[7, 1, 23],
[8, 4, 23],
[0, 6, 22],
[1, 0, 5],
[4, 3, 5],
[1, 0, 23],
[4, 3, 22],
[10, 7, 14],
[6, 8, 18],
[8, 6, 22],
[7, 10, 23],
[4, 3, 11],
[1, 0, 11],
[1, 0, 22],
[4, 3, 23],
[10, 7, 18],
[6, 8, 14],
[8, 6, 23],
[7, 10, 22],
[6, 7, 11],
[10, 8, 11],
[8, 1, 23],
[0, 10, 22],
[3, 6, 22],
[7, 4, 23],
[4, 3, 2],
[1, 0, 2],
[10, 8, 2],
[6, 7, 2],
[4, 3, 9],
[1, 0, 9],
[10, 8, 9],
[6, 7, 9],
[4, 8, 14],
[6, 0, 18],
[10, 3, 18],
[1, 7, 14],
[4, 8, 18],
[6, 0, 14],
[10, 3, 14],
[1, 7, 18],
[6, 7, 5],
[10, 8, 5],
[6, 8, 5],
[10, 7, 5],
[8, 1, 22],
[0, 10, 23],
[3, 6, 23],
[7, 4, 22],
[4, 24, 2],
[25, 3, 2],
[4, 24, 26],
[25, 3, 27],
[4, 24, 27],
[25, 3, 26],
[28, 29, 26], [30, 31, 26],
[32, 33, 26],
[34, 35, 27],
[36, 37, 27],
[38, 39, 27],
[2, 0, 1],
[1, 2, 0],
[1, 25, 5],
[24, 0, 5],
[39, 36, 40],
[35, 38, 40],
[37, 34, 40],
[33, 30, 41],
[29, 32, 41],
[31, 28, 41],
[5, 3, 4],
[4, 5, 3],
[25, 1, 5],
[0, 24, 5],
[24, 4, 5],
[3, 25, 5],
[4, 3, 41],
[25, 1, 40],
[24, 4, 41],
[3, 25, 40],
[4, 3, 40],
[25, 1, 41],
[24, 4, 40],
[3, 25, 41],
[35, 34, 40],
[37, 36, 40],
[39, 38, 40],
[29, 28, 41],
[31, 30, 41],
[33, 32, 41],
[3, 5, 4],
[5, 4, 3],
[25, 1, 2],
[0, 24, 2],
[24, 4, 2],
[3, 25, 2],
[25, 1, 9],
[0, 24, 9],
[24, 4, 9],
[3, 25, 9],
[30, 33, 26],
[32, 29, 26],
[28, 31, 26],
[36, 39, 27],
[38, 35, 27],
[34, 37, 27],
[0, 2, 1],
[2, 1, 0],
[30, 33, 42],
[32, 29, 42],
[28, 31, 42],
[36, 39, 43],
[38, 35, 43],
[34, 37, 43],
[7, 9, 6],
[9, 6, 7],
[25, 1, 11],
[0, 24, 11],
[24, 4, 11],
[3, 25, 11],
[35, 34, 44],
[37, 36, 44],
[39, 38, 44],
[29, 28, 45],
[31, 30, 45], [33, 32, 45],
[8, 11, 10],
[11, 10, 8],
[1, 25, 2],
[24, 0, 2],
[1, 25, 42],
[24, 0, 43],
[1, 25, 43],
[24, 0, 42],
[1, 25, 27],
[24, 0, 26],
[1, 25, 26],
[24, 0, 27],
[1, 25, 9],
[24, 0, 9],
[4, 24, 5],
[25, 3, 5],
[4, 24, 11],
[25, 3, 11],
[1, 0, 40],
[4, 3, 44],
[0, 24, 45],
[1, 0, 41],
[4, 3, 45],
[0, 24, 44],
[0, 24, 40],
[0, 24, 41],
[2, 3, 4],
[5, 3, 1],
[5, 0, 4],
[4, 2, 3],
[1, 5, 3],
[4, 5, 0],
[2, 7, 6],
[2, 8, 10],
[5, 8, 6],
[5, 7, 10],
[1, 9, 7],
[4, 9, 8],
[1, 11, 8],
[4, 11, 7],
[9, 0, 6],
[9, 3, 10],
[11, 3, 6],
[11, 0, 10],
[6, 2, 7],
[10, 2, 8],
[6, 5, 8],
[10, 5, 7],
[9, 7, 1],
[9, 8, 4],
[11, 8, 1],
[11, 7, 4],
[6, 9, 0],
[10, 9, 3],
[6, 11, 3],
[10, 11, 0],
[9, 7, 6],
[9, 8, 10],
[11, 8, 6],
[11, 7, 10],
[6, 9, 7],
[10, 9, 8],
[6, 11, 8],
[10, 11, 7],
[2, 3, 10],
[5, 8, 1],
[11, 0, 4],
[10, 2, 3],
[1, 5, 8], [4, 11, 0],
[5, 0, 1],
[2, 0, 4],
[2, 3, 1],
[1, 5, 0],
[4, 2, 0],
[1, 2, 3],
[11, 8, 10],
[11, 7, 6],
[9, 7, 10],
[9, 8, 6],
[10, 11, 8],
[6, 11, 7],
[10, 9, 7],
[6, 9, 8],
[5, 8, 10],
[5, 7, 6],
[2, 7, 10],
[2, 8, 6],
[4, 11, 8],
[1, 11, 7],
[4, 9, 7],
[1, 9, 8],
[11, 3, 10],
[11, 0, 6],
[9, 0, 10],
[9, 3, 6],
[10, 5, 8],
[6, 5, 7],
[10, 2, 7],
[6, 2, 8],
[11, 8, 4],
[11, 7, 1],
[9, 7, 4],
[9, 8, 1],
[10, 11, 3],
[6, 11, 0],
[10, 9, 0],
[6, 9, 3],
[22, 15, 13],
[22, 12, 16],
[14, 12, 13],
[14, 15, 16],
[13, 22, 15],
[16, 22, 12],
[13, 14, 12],
[16, 14, 15],
[22, 21, 17],
[22, 20, 19],
[14, 20, 17],
[14, 21, 19],
[13, 23, 21],
[16, 23, 20],
[13, 18, 20],
[16, 18, 21],
[23, 15, 17],
[23, 12, 19],
[18, 12, 17],
[18, 15, 19],
[17, 22, 21],
[19, 22, 20],
[17, 14, 20],
[19, 14, 21],
[23, 21, 13],
[23, 20, 16],
[18, 20, 13],
[18, 21, 16],
[17, 23, 15],
[19, 23, 12],
[17, 18, 12], [19, 18, 15],
[5, 0, 6],
[2, 7, 4],
[9, 3, 1],
[6, 5, 0],
[4, 2, 7],
[1, 9, 3],
[0, 2, 4],
[3, 2, 1],
[0, 5, 1],
[2, 1, 3],
[2, 4, 0],
[5, 1, 0],
[7, 9, 10],
[8, 9, 6],
[7, 11, 6],
[9, 6, 8],
[9, 10, 7],
[11, 6, 7],
[1, 7, 11],
[4, 8, 11],
[1, 8, 9],
[4, 7, 9],
[0, 9, 10],
[3, 9, 6],
[3, 11, 10],
[0, 11, 6],
[2, 6, 8],
[2, 10, 7],
[5, 6, 7],
[5, 10, 8],
[6, 0, 11],
[10, 3, 11],
[6, 3, 9],
[10, 0, 9],
[7, 2, 10],
[8, 2, 6],
[8, 5, 10],
[7, 5, 6],
[9, 1, 8],
[9, 4, 7],
[11, 1, 7],
[11, 4, 8],
[7, 9, 4],
[8, 9, 1],
[8, 11, 4],
[7, 11, 1],
[9, 6, 3],
[9, 10, 0],
[11, 6, 0],
[11, 10, 3],
[19, 12, 23],
[13, 15, 22],
[16, 21, 18],
[17, 20, 14],
[20, 14, 17],
[21, 18, 16],
[15, 22, 13],
[12, 23, 19],
[18, 16, 21],
[14, 17, 20],
[23, 19, 12],
[22, 13, 15],
[19, 20, 22],
[13, 21, 23],
[16, 15, 14],
[17, 12, 18],
[20, 18, 13],
[21, 14, 19],
[15, 23, 17], [12, 22, 16],
[18, 19, 15],
[14, 13, 12],
[23, 16, 20],
[22, 17, 21],
[16, 12, 22],
[17, 15, 23],
[19, 21, 14],
[13, 20, 18],
[12, 14, 13],
[15, 18, 19],
[21, 22, 17],
[20, 23, 16],
[14, 16, 15],
[18, 17, 12],
[22, 19, 20],
[23, 13, 21],
[16, 20, 23],
[17, 21, 22],
[19, 15, 18],
[13, 12, 14],
[12, 18, 17],
[15, 14, 16],
[21, 23, 13],
[20, 22, 19],
[14, 19, 21],
[18, 13, 20],
[22, 16, 12],
[23, 17, 15],
[19, 12, 22],
[17, 21, 23],
[16, 15, 18],
[13, 20, 14],
[20, 14, 13],
[15, 18, 16],
[21, 23, 17],
[12, 22, 19],
[18, 16, 15],
[14, 13, 20],
[22, 19, 12],
[23, 17, 21],
[3, 2, 4],
[3, 5, 1],
[0, 5, 4],
[2, 4, 3],
[5, 1, 3],
[5, 4, 0],
[1, 7, 9],
[4, 8, 9],
[1, 8, 11],
[4, 7, 11],
[0, 9, 6],
[3, 9, 10],
[3, 11, 6],
[0, 11, 10],
[2, 6, 7],
[2, 10, 8],
[5, 6, 8],
[5, 10, 7],
[6, 0, 9],
[10, 3, 9],
[6, 3, 11],
[10, 0, 11],
[7, 2, 6],
[8, 2, 10],
[8, 5, 6],
[7, 5, 10],
[9, 1, 7],
[9, 4, 8],
[11, 1, 8], [11, 4, 7],
[7, 9, 1],
[8, 9, 4],
[8, 11, 1],
[7, 11, 4],
[9, 6, 0],
[9, 10, 3],
[11, 6, 3],
[11, 10, 0],
[8, 9, 10],
[8, 11, 6],
[7, 11, 10],
[9, 10, 8],
[11, 6, 8],
[11, 10, 7],
[6, 0, 2],
[10, 3, 2],
[6, 3, 5],
[10, 0, 5],
[7, 2, 1],
[8, 2, 4],
[8, 5, 1],
[7, 5, 4],
[9, 1, 0],
[9, 4, 3],
[11, 1, 3],
[11, 4, 0],
[1, 7, 2],
[4, 8, 2],
[1, 8, 5],
[4, 7, 5],
[0, 9, 1],
[3, 9, 4],
[3, 11, 1],
[0, 11, 4],
[2, 6, 0],
[2, 10, 3],
[5, 6, 3],
[5, 10, 0],
[0, 2, 6],
[3, 2, 10],
[3, 5, 6],
[0, 5, 10],
[2, 1, 7],
[2, 4, 8],
[5, 1, 8],
[5, 4, 7],
[16, 12, 14],
[13, 21, 18],
[19, 15, 23],
[17, 20, 22],
[12, 14, 16],
[21, 18, 13],
[15, 23, 19],
[20, 22, 17],
[14, 16, 12],
[18, 13, 21],
[23, 19, 15],
[22, 17, 20],
[19, 20, 18],
[17, 15, 14],
[16, 21, 22],
[13, 12, 23],
[20, 18, 19],
[15, 14, 17],
[21, 22, 16],
[12, 23, 13],
[18, 19, 20],
[14, 17, 15],
[22, 16, 21], [23, 13, 12],
[6, 0, 5],
[10, 3, 5],
[6, 3, 2],
[10, 0, 2],
[7, 2, 4],
[8, 2, 1],
[8, 5, 4],
[7, 5, 1],
[9, 1, 3],
[9, 4, 0],
[11, 1, 0],
[11, 4, 3],
[1, 7, 5],
[4, 8, 5],
[1, 8, 2],
[4, 7, 2],
[0, 9, 4],
[3, 9, 1],
[3, 11, 4],
[0, 11, 1],
[2, 6, 3],
[2, 10, 0],
[5, 6, 0],
[5, 10, 3],
[0, 2, 10],
[3, 2, 6],
[3, 5, 10],
[0, 5, 6],
[2, 1, 8],
[2, 4, 7],
[5, 1, 7],
[5, 4, 8],
[21, 17, 23],
[20, 16, 22],
[12, 13, 18],
[15, 19, 14],
[23, 21, 17],
[22, 20, 16],
[18, 12, 13],
[14, 15, 19],
[17, 23, 21],
[16, 22, 20],
[13, 18, 12],
[19, 14, 15],
[21, 13, 22],
[20, 19, 23],
[12, 17, 14],
[15, 16, 18],
[23, 15, 13],
[22, 12, 19],
[18, 20, 17],
[14, 21, 16],
[17, 22, 15],
[16, 23, 12],
[13, 14, 20],
[19, 18, 21],
[15, 17, 22],
[12, 16, 23],
[20, 13, 14],
[21, 19, 18],
[22, 21, 13],
[23, 20, 19],
[14, 12, 17],
[18, 15, 16],
[13, 23, 15],
[19, 22, 12],
[17, 18, 20],
[16, 14, 21],
[15, 13, 23], [12, 19, 22],
[20, 17, 18],
[21, 16, 14],
[22, 15, 17],
[23, 12, 16],
[14, 20, 13],
[18, 21, 19],
[13, 22, 21],
[19, 23, 20],
[17, 14, 12],
[16, 18, 15],
[6, 5, 3],
[4, 9, 3],
[9, 3, 4],
[5, 7, 4],
[4, 5, 7],
[5, 3, 6],
];
export const GroupData = [
[0],
[0, 1],
[0, 2],
[0, 3],
[0, 2, 4, 5],
[0, 6],
[0, 7],
[0, 6, 4, 8],
[0, 7, 4, 9],
[0, 6, 2, 1],
[0, 3, 1, 10],
[0, 6, 2, 1, 4, 8, 5, 11],
[0, 12, 1, 7],
[0, 1, 13, 14],
[0, 12, 1, 7, 4, 15, 11, 9],
[0, 16, 2, 17],
[0, 18, 12, 17],
[0, 16, 5, 19],
[0, 20, 13, 19],
[0, 18, 12, 17, 4, 21, 15, 19],
[0, 16, 2, 17, 4, 22, 5, 19],
[0, 16, 2, 17, 23, 24, 13, 25, 26, 20, 27, 28, 4, 22, 5, 19],
[0, 16, 17, 2, 29, 21, 30, 15],
[0, 20, 13, 19, 29, 31, 32, 33],
[0, 16, 6, 34],
[0, 18, 7, 34],
[0, 16, 7, 35],
[0, 16, 36, 37],
[0, 18, 36, 38],
[0, 16, 14, 39],
[0, 20, 40, 34],
[0, 16, 8, 41],
[0, 18, 8, 42],
[0, 16, 9, 42],
[0, 16, 6, 34, 4, 22, 8, 41],
[0, 18, 7, 34, 4, 21, 9, 41],
[0, 16, 7, 35, 4, 22, 9, 42],
[0, 16, 6, 34, 23, 24, 14, 39],
[0, 16, 10, 43, 23, 24, 7, 35],
[0, 16, 36, 37, 23, 24, 9, 42],
[0, 16, 8, 41, 23, 24, 40, 38],
[0, 16, 6, 34, 23, 24, 14, 39, 26, 20, 40, 38, 4, 22, 8, 41],
[0, 16, 44, 45, 23, 24, 46, 47, 26, 20, 48, 49, 4, 22, 50, 51],
[0, 16, 6, 34, 29, 21, 9, 42],
[0, 16, 8, 41, 29, 21, 7, 35],
[0, 16, 36, 37, 29, 21, 14, 39],
[0, 16, 2, 17, 1, 52, 6, 34],
[0, 16, 2, 17, 53, 54, 9, 42],
[0, 16, 12, 33, 1, 52, 7, 35],
[0, 16, 2, 17, 11, 55, 8, 41], [0, 56, 2, 57, 1, 58, 6, 37],
[0, 56, 15, 25, 1, 58, 9, 39],
[0, 20, 27, 17, 1, 59, 40, 34],
[0, 56, 12, 28, 1, 58, 7, 38],
[0, 16, 5, 19, 1, 52, 8, 41],
[0, 22, 13, 28, 1, 55, 14, 38],
[0, 18, 13, 60, 1, 61, 14, 43],
[0, 16, 15, 30, 1, 52, 9, 42],
[0, 16, 5, 19, 11, 55, 6, 34],
[0, 21, 12, 19, 1, 54, 7, 41],
[0, 20, 13, 19, 1, 59, 14, 41],
[0, 20, 3, 30, 1, 59, 10, 42],
[0, 18, 12, 17, 1, 61, 7, 34, 4, 21, 15, 19, 11, 54, 9, 41],
[0, 24, 13, 17, 1, 62, 14, 34, 4, 20, 27, 19, 11, 59, 40, 41],
[0, 16, 2, 17, 1, 52, 6, 34, 4, 22, 5, 19, 11, 55, 8, 41],
[0, 16, 12, 33, 1, 52, 7, 35, 4, 22, 15, 30, 11, 55, 9, 42],
[0, 31, 3, 17, 1, 63, 10, 34, 4, 56, 32, 19, 11, 58, 36, 41],
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[0, 24, 5, 28, 158, 265, 258, 275, 159, 277, 270, 263, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 66, 69, 50, 49, 332, 349, 342, 359, 336, 361, 354, 347, 493, 123, 483, 140, 498, 507, 204, 485, 503, 490, 509, 205, 23, 16, 27, 19, 256, 273, 251, 267, 260, 269, 278, 255, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 68, 67, 48, 51, 340, 357, 334, 351, 344, 353, 362, 339, 124, 480, 89, 494, 506, 499, 484, 474, 511, 478, 501, 488, 26, 22, 13, 17, 264, 250, 274, 259, 268, 261, 254, 279, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 70, 73, 46, 45, 348, 333, 358, 343, 352, 345, 338, 363, 122, 492, 141, 482, 475, 487, 496, 505, 479, 510, 489, 500, 4, 20, 2, 25, 272, 257, 266, 252, 276, 253, 262, 271, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 72, 71, 44, 47, 356, 341, 350, 335, 360, 337, 346, 355, 481, 125, 495, 88, 486, 476, 504, 497, 491, 502, 477, 508],
[0, 24, 5, 28, 158, 265, 258, 275, 159, 277, 270, 263, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 531, 129, 521, 92, 536, 545, 212, 523, 541, 528, 547, 213, 23, 16, 27, 19, 256, 273, 251, 267, 260, 269, 278, 255, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 126, 518, 91, 532, 544, 537, 522, 512, 549, 516, 539, 526, 26, 22, 13, 17, 264, 250, 274, 259, 268, 261, 254, 279, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 128, 530, 93, 520, 513, 525, 534, 543, 517, 548, 527, 538, 4, 20, 2, 25, 272, 257, 266, 252, 276, 253, 262, 271, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 519, 127, 533, 90, 524, 514, 542, 535, 529, 540, 515, 546],
[0, 16, 2, 17, 158, 250, 251, 252, 159, 253, 254, 255, 100, 101, 75, 74, 370, 371, 188, 372, 373, 374, 375, 189, 1, 52, 6, 34, 168, 294, 295, 296, 169, 297, 298, 299, 122, 123, 89, 88, 475, 476, 204, 474, 479, 478, 477, 205, 29, 21, 15, 30, 280, 281, 282, 283, 284, 285, 286, 287, 116, 117, 83, 82, 376, 377, 224, 378, 379, 380, 381, 225, 53, 54, 9, 42, 300, 301, 302, 303, 304, 305, 306, 307, 128, 129, 91, 90, 513, 514, 212, 512, 517, 516, 515, 213],
[0, 20, 13, 19, 158, 273, 266, 259, 159, 261, 278, 271, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 1, 59, 14, 41, 168, 325, 318, 311, 169, 313, 330, 323, 551, 550, 553, 552, 556, 557, 554, 555, 561, 560, 559, 558, 29, 31, 32, 33, 280, 288, 289, 290, 284, 291, 292, 293, 450, 415, 440, 429, 454, 431, 420, 445, 458, 447, 436, 425, 53, 63, 36, 35, 300, 364, 365, 366, 304, 367, 368, 369, 563, 562, 565, 564, 568, 569, 566, 567, 573, 572, 571, 570],
[0, 16],
[0, 18],
[0, 16, 26, 20],
[0, 2, 23, 13],
[0, 3, 4, 32],
[0, 2, 29, 15],
[0, 3, 29, 27],
[0, 52],
[0, 63],
[0, 52, 26, 59],
[0, 63, 26, 54],
[0, 52, 16, 1],
[0, 18, 1, 61],
[0, 52, 16, 1, 26, 59, 20, 65],
[0, 31, 1, 63],
[0, 1, 24, 62],
[0, 15, 1, 9], // 'P 1 21/n 1'
// X,Y,Z
// -X+1/2,Y+1/2,-Z+1/2
// -X,-Y,-Z
// X+1/2,-Y+1/2,Z+1/2
[0, 5, 1, 8], // 'P 1 21/a 1'
// X,Y,Z // -X+1/2,Y+1/2,-Z
// -X,-Y,-Z
// X+1/2,-Y+1/2,Z
[0, 31, 1, 63, 26, 21, 65, 54],
[0, 2, 57, 56],
[0, 60, 3, 16],
[0, 22, 57, 3],
[0, 2, 28, 20],
[0, 17, 13, 24],
[0, 20, 19, 13, 4, 24, 17, 27],
[0, 22, 57, 3, 4, 16, 60, 32],
[0, 22, 57, 3, 23, 20, 30, 12, 26, 24, 33, 15, 4, 16, 60, 32],
[0, 22, 57, 3, 29, 18, 27, 25],
[0, 22, 3, 57, 1, 55, 10, 37],
[0, 22, 385, 396, 3, 57, 109, 117],
[0, 22, 57, 3, 159, 279, 654, 655, 158, 274, 656, 657, 29, 18, 25, 27, 284, 658, 262, 269, 280, 659, 257, 267],
];
export const SpacegroupNameToIndexMap = {
'P 1': 0,
'P -1': 1,
'P 1 2 1': 2,
'P 1 21 1': 3,
'C 1 2 1': 4,
'P 1 m 1': 5,
'P 1 c 1': 6,
'C 1 m 1': 7,
'C 1 c 1': 8,
'P 1 2/m 1': 9,
'P 1 21/m 1': 10,
'C 1 2/m 1': 11,
'P 1 2/c 1': 12,
'P 1 21/c 1': 13,
'C 1 2/c 1': 14,
'P 2 2 2': 15,
'P 2 2 21': 16,
'P 21 21 2': 17,
'P 21 21 21': 18,
'C 2 2 21': 19,
'C 2 2 2': 20,
'F 2 2 2': 21,
'I 2 2 2': 22,
'I 21 21 21': 23,
'P m m 2': 24,
'P m c 21': 25,
'P c c 2': 26,
'P m a 2': 27,
'P c a 21': 28,
'P n c 2': 29,
'P m n 21': 30,
'P b a 2': 31,
'P n a 21': 32,
'P n n 2': 33,
'C m m 2': 34,
'C m c 21': 35,
'C c c 2': 36,
'A m m 2': 37,
'A b m 2': 38,
'A m a 2': 39,
'A b a 2': 40,
'F m m 2': 41,
'F d d 2': 42,
'I m m 2': 43,
'I b a 2': 44,
'I m a 2': 45,
'P 2/m 2/m 2/m': 46,
'P m m m': 46,
'P 2/n 2/n 2/n': 47,
'P n n n': 47,
'P 2/c 2/c 2/m': 48, 'P c c m': 48,
'P 2/b 2/a 2/n': 49,
'P b a n': 49,
'P 21/m 2/m 2/a': 50,
'P m m a': 50,
'P 2/n 21/n 2/a': 51,
'P n n a': 51,
'P 2/m 2/n 21/a': 52,
'P m n a': 52,
'P 21/c 2/c 2/a': 53,
'P c c a': 53,
'P 21/b 21/a 2/m': 54,
'P b a m': 54,
'P 21/c 21/c 2/n': 55,
'P c c n': 55,
'P 2/b 21/c 21/m': 56,
'P b c m': 56,
'P 21/n 21/n 2/m': 57,
'P n n m': 57,
'P 21/m 21/m 2/n': 58,
'P m m n': 58,
'P 21/b 2/c 21/n': 59,
'P b c n': 59,
'P 21/b 21/c 21/a': 60,
'P b c a': 60,
'P 21/n 21/m 21/a': 61,
'P n m a': 61,
'C 2/m 2/c 21/m': 62,
'C m c m': 62,
'C 2/m 2/c 21/a': 63,
'C m c a': 63,
'C 2/m 2/m 2/m': 64,
'C m m m': 64,
'C 2/c 2/c 2/m': 65,
'C c c m': 65,
'C 2/m 2/m 2/a': 66,
'C m m a': 66,
'C 2/c 2/c 2/a': 67,
'C c c a': 67,
'F 2/m 2/m 2/m': 68,
'F m m m': 68,
'F 2/d 2/d 2/d': 69,
'F d d d': 69,
'I 2/m 2/m 2/m': 70,
'I m m m': 70,
'I 2/b 2/a 2/m': 71,
'I b a m': 71,
'I 21/b 21/c 21/a': 72,
'I b c a': 72,
'I 21/m 21/m 21/a': 73,
'I m m a': 73,
'P 4': 74,
'P 41': 75,
'P 42': 76,
'P 43': 77,
'I 4': 78,
'I 41': 79,
'P -4': 80,
'I -4': 81,
'P 4/m': 82,
'P 42/m': 83,
'P 4/n': 84,
'P 42/n': 85,
'I 4/m': 86,
'I 41/a': 87,
'P 4 2 2': 88,
'P 4 21 2': 89,
'P 41 2 2': 90,
'P 41 21 2': 91,
'P 42 2 2': 92, 'P 42 21 2': 93,
'P 43 2 2': 94,
'P 43 21 2': 95,
'I 4 2 2': 96,
'I 41 2 2': 97,
'P 4 m m': 98,
'P 4 b m': 99,
'P 42 c m': 100,
'P 42 n m': 101,
'P 4 c c': 102,
'P 4 n c': 103,
'P 42 m c': 104,
'P 42 b c': 105,
'I 4 m m': 106,
'I 4 c m': 107,
'I 41 m d': 108,
'I 41 c d': 109,
'P -4 2 m': 110,
'P -4 2 c': 111,
'P -4 21 m': 112,
'P -4 21 c': 113,
'P -4 m 2': 114,
'P -4 c 2': 115,
'P -4 b 2': 116,
'P -4 n 2': 117,
'I -4 m 2': 118,
'I -4 c 2': 119,
'I -4 2 m': 120,
'I -4 2 d': 121,
'P 4/m 2/m 2/m': 122,
'P4/m m m': 122,
'P 4/m 2/c 2/c': 123,
'P4/m c c': 123,
'P 4/n 2/b 2/m': 124,
'P4/n b m': 124,
'P 4/n 2/n 2/c': 125,
'P4/n n c': 125,
'P 4/m 21/b 2/m': 126,
'P4/m b m': 126,
'P 4/m 21/n 2/c': 127,
'P4/m n c': 127,
'P 4/n 21/m 2/m': 128,
'P4/n m m': 128,
'P 4/n 2/c 2/c': 129,
'P4/n c c': 129,
'P 42/m 2/m 2/c': 130,
'P42/m m c': 130,
'P 42/m 2/c 2/m': 131,
'P42/m c m': 131,
'P 42/n 2/b 2/c': 132,
'P42/n b c': 132,
'P 42/n 2/n 2/m': 133,
'P42/n n m': 133,
'P 42/m 21/b 2/c': 134,
'P42/m b c': 134,
'P 42/m 21/n 2/m': 135,
'P42/m n m': 135,
'P 42/n 21/m 2/c': 136,
'P42/n m c': 136,
'P 42/n 21/c 2/m': 137,
'P42/n c m': 137,
'I 4/m 2/m 2/m': 138,
'I4/m m m': 138,
'I 4/m 2/c 2/m': 139,
'I4/m c m': 139,
'I 41/a 2/m 2/d': 140,
'I41/a m d': 140,
'I 41/a 2/c 2/d': 141,
'I41/a c d': 141,
'P 3': 142, 'P 31': 143,
'P 32': 144,
'H 3': 145,
'R 3': 146,
'P -3': 147,
'H -3': 148,
'R -3': 149,
'P 3 1 2': 150,
'P 3 2 1': 151,
'P 31 1 2': 152,
'P 31 2 1': 153,
'P 32 1 2': 154,
'P 32 2 1': 155,
'H 3 2': 156,
'R 3 2': 157,
'P 3 m 1': 158,
'P 3 1 m': 159,
'P 3 c 1': 160,
'P 3 1 c': 161,
'H 3 m': 162,
'R 3 m': 163,
'H 3 c': 164,
'R 3 c': 165,
'P -3 1 2/m': 166,
'P -3 1 m': 166,
'P -3 1 2/c': 167,
'P -3 1 c': 167,
'P -3 2/m 1': 168,
'P -3 m 1': 168,
'P -3 2/c 1': 169,
'P -3 c 1': 169,
'H -3 2/m': 170,
'H -3 m': 170,
'R -3 2/m': 171,
'R -3 m': 171,
'H -3 2/c': 172,
'H -3 c': 172,
'R -3 2/c': 173,
'R -3 c': 173,
'P 6': 174,
'P 61': 175,
'P 65': 176,
'P 62': 177,
'P 64': 178,
'P 63': 179,
'P -6': 180,
'P 6/m': 181,
'P 63/m': 182,
'P 6 2 2': 183,
'P 61 2 2': 184,
'P 65 2 2': 185,
'P 62 2 2': 186,
'P 64 2 2': 187,
'P 63 2 2': 188,
'P 6 m m': 189,
'P 6 c c': 190,
'P 63 c m': 191,
'P 63 m c': 192,
'P -6 m 2': 193,
'P -6 c 2': 194,
'P -6 2 m': 195,
'P -6 2 c': 196,
'P 6/m 2/m 2/m': 197,
'P 6/m m m': 197,
'P 6/m 2/c 2/c': 198,
'P 6/m c c': 198,
'P 63/m 2/c 2/m': 199,
'P 63/m c m': 199,
'P 63/m 2/m 2/c': 200,
'P 63/m m c': 200, 'P 2 3': 201,
'F 2 3': 202,
'I 2 3': 203,
'P 21 3': 204,
'I 21 3': 205,
'P 2/m -3': 206,
'P m -3': 206,
'P 2/n -3': 207,
'P n -3': 207,
'F 2/m -3': 208,
'F m -3': 208,
'F 2/d -3': 209,
'F d -3': 209,
'I 2/m -3': 210,
'I m -3': 210,
'P 21/a -3': 211,
'P a -3': 211,
'I 21/a -3': 212,
'I a -3': 212,
'P 4 3 2': 213,
'P 42 3 2': 214,
'F 4 3 2': 215,
'F 41 3 2': 216,
'I 4 3 2': 217,
'P 43 3 2': 218,
'P 41 3 2': 219,
'I 41 3 2': 220,
'P -4 3 m': 221,
'F -4 3 m': 222,
'I -4 3 m': 223,
'P -4 3 n': 224,
'F -4 3 c': 225,
'I -4 3 d': 226,
'P 4/m -3 2/m': 227,
'P m -3 m': 227,
'P 4/n -3 2/n': 228,
'P n -3 n': 228,
'P 42/m -3 2/n': 229,
'P m -3 n': 229,
'P 42/n -3 2/m': 230,
'P n -3 m': 230,
'F 4/m -3 2/m': 231,
'F m -3 m': 231,
'F 4/m -3 2/c': 232,
'F m -3 c': 232,
'F 41/d -3 2/m': 233,
'F d -3 m': 233,
'F 41/d -3 2/c': 234,
'F d -3 c': 234,
'I 4/m -3 2/m': 235,
'I m -3 m': 235,
'I 41/a -3 2/d': 236,
'I a -3 d': 236,
'P 1 1 2': 237,
'P 1 1 21': 238,
'B 1 1 2': 239,
'B 2': 239,
'A 1 2 1': 240,
'C 1 21 1': 241,
'I 1 2 1': 242,
'I 2': 242,
'I 1 21 1': 243,
'P 1 1 m': 244,
'P 1 1 b': 245,
'B 1 1 m': 246,
'B 1 1 b': 247,
'P 1 1 2/m': 248,
'P 1 1 21/m': 249,
'B 1 1 2/m': 250,
'P 1 1 2/b': 251, 'P 1 1 21/b': 252,
'P 1 21/n 1': 253,
'P 1 21/a 1': 254,
'B 1 1 2/b': 255,
'P 21 2 2': 256,
'P 2 21 2': 257,
'P 21 21 2 (a)': 258,
'P 21 2 21': 259,
'P 2 21 21': 260,
'C 2 2 21a)': 261,
'C 2 2 2a': 262,
'F 2 2 2a': 263,
'I 2 2 2a': 264,
'P 21/m 21/m 2/n a': 265,
'P 42 21 2a': 266,
'I 2 3a': 267,
};
export function getSpacegroupIndexFromNumber(num: number) {
// 38 spacegroup variants as given CCP4s symop.lib
switch (num) {
case 1146: return 146
case 1148: return 149
case 1155: return 157
case 1160: return 163
case 1161: return 165
case 1166: return 171
case 1167: return 173
case 1003: return 237 // 'P 1 1 2' !(dyad along z)
case 1004: return 238 // 'P 1 1 21' !(unique axis c)
case 1005: return 239 // 'B 1 1 2' 'B 2'
case 2005: return 240 // 'A 1 2 1'
case 3005: return 241 // 'C 1 21 1' ! (Origin on screw at 1/4X)
case 4005: return 242 // 'I 1 2 1' 'I 2' !!! GJK @ 2003-06-02
case 5005: return 243 // 'I 1 21 1'
case 1006: return 244 // 'P 1 1 m'
case 1007: return 245 // 'P 1 1 b'
case 1008: return 246 // 'B 1 1 m'
case 1009: return 247 // 'B 1 1 b'
case 1010: return 248 // 'P 1 1 2/m'
case 1011: return 249 // 'P 1 1 21/m'
case 1012: return 250 // 'B 1 1 2/m'
case 1013: return 251 // 'P 1 1 2/b'
case 1014: return 252 // 'P 1 1 21/b'
case 2014: return 253 // 'P 1 21/n 1'
case 3014: return 254 // 'P 1 21/a 1'
case 1015: return 255 // 'B 1 1 2/b'
case 1017: return 256 // 'P 21 2 2' !(unique axis a)
case 2017: return 257 // 'P 2 21 2' !(unique axis b)
case 1018: return 258 // 'P 21 21 2 (a)' ! origin on 21 21, shift (1/4,1/4,0)
case 2018: return 259 // 'P 21 2 21' !(unique axis b)
case 3018: return 260 // 'P 2 21 21' !(unique axis a)
case 1020: return 261 // 'C 2 2 21a)' ! P212121 with C centring, shift(1/4,0,0)
case 1021: return 262 // 'C 2 2 2a' ! C21212a origin on 21 21
case 1022: return 263 // 'F 2 2 2a' ! same as 1018 with face centring shift (1/4,0,0)
case 1023: return 264 // 'I 2 2 2a' ! as 1018 with origin shift (1/4,1/4,1/4)
case 1059: return 265 // 'P 21/m 21/m 2/n a'
case 1094: return 266 // 'P 42 21 2a' ! (as P21212a) origin on 21 21 ie Shift 1/4,1/4,1/4
case 1197: return 267 // 'I 2 3a' ! Expansion of 1023 which is an expansion of 1018
}
let offset = 0
if (num > 146) ++offset
if (num > 148) ++offset
if (num > 155) ++offset
if (num > 160) ++offset
if (num > 161) ++offset
if (num > 166) ++offset
if (num > 167) ++offset
return num - 1 + offset
}
export function getSpacegroupNumberFromIndex(idx: number) {
if (idx < 146) return idx + 1
if (idx === 146) return 1146
if (idx < 149) return idx + 1 - 1
if (idx === 149) return 1148
if (idx < 157) return idx + 1 - 2
if (idx === 157) return 1155
if (idx < 163) return idx + 1 - 3
if (idx === 163) return 1160
if (idx < 165) return idx + 1 - 4
if (idx === 165) return 1161
if (idx < 171) return idx + 1 - 5
if (idx === 171) return 1166
if (idx < 173) return idx + 1 - 6
if (idx === 173) return 1167
if (idx < 237) return idx + 1 - 7
if (idx === 237) return 1003
if (idx === 238) return 1004
if (idx === 239) return 1005
if (idx === 240) return 2005
if (idx === 241) return 3005
if (idx === 242) return 4005
if (idx === 243) return 5005
if (idx === 244) return 1006
if (idx === 245) return 1007
if (idx === 246) return 1008
if (idx === 247) return 1009
if (idx === 248) return 1010
if (idx === 249) return 1011
if (idx === 250) return 1012
if (idx === 251) return 1013
if (idx === 252) return 1014
if (idx === 253) return 2014
if (idx === 254) return 3014
if (idx === 255) return 1015
if (idx === 256) return 1017
if (idx === 257) return 2017
if (idx === 258) return 1018
if (idx === 259) return 2018
if (idx === 260) return 3018
if (idx === 261) return 1020
if (idx === 262) return 1021
if (idx === 263) return 1022
if (idx === 264) return 1023
if (idx === 265) return 1059
if (idx === 266) return 1094
if (idx === 267) return 1197
throw new Error(`unknown spacegroup index '${idx}'`)
}
export type SpacegroupName = keyof typeof SpacegroupNameToIndexMap
/** Maps spacegroup index to Hermann-Mauguin spacegroup name */
export const SpacegroupName: { [idx: number]: SpacegroupName } = (function () {
const names = Object.create(null);
for (const n of Object.keys(SpacegroupNameToIndexMap)) {
names[(SpacegroupNameToIndexMap as any)[n]] = n; }
return names;
}());
/** Maps spacegroup index to spacegroup number from International Tables for Crystallography */
export const SpacegroupNumber: { [idx: number]: number } = (function () {
const numbers = Object.create(null);
for (const n of Object.keys(SpacegroupNameToIndexMap)) {
const idx = (SpacegroupNameToIndexMap as any)[n]
numbers[idx] = getSpacegroupNumberFromIndex(idx);
}
return numbers;
}());
/** return -1 if the spacegroup does not exist */
export function getSpacegroupIndex(nameOrNumber: number | string | SpacegroupName): number {
const index = typeof nameOrNumber === 'number'
? getSpacegroupIndexFromNumber(nameOrNumber)
: SpacegroupNameToIndexMap[nameOrNumber as SpacegroupName];
if (typeof index === 'undefined' || typeof SpacegroupName[index] === 'undefined') return -1;
return index;
}