.. _program_listing_file_src_spg_database.cpp: Program Listing for File spg_database.cpp ========================================= |exhale_lsh| :ref:`Return to documentation for file ` (``src/spg_database.cpp``) .. |exhale_lsh| unicode:: U+021B0 .. UPWARDS ARROW WITH TIP LEFTWARDS .. code-block:: cpp /* This file is part of brille. Copyright © 2019,2020 Greg Tucker brille is free software: you can redistribute it and/or modify it under the terms of the GNU Affero General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. brille 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 Affero General Public License for more details. You should have received a copy of the GNU Affero General Public License along with brille. If not, see . */ /* This file has evolved from spg_database.cpp distributed as part of spglib. Changes have been made to introduce C++ style classes as well as other modifications to suit the needs of brille. spglib was licensed under the following BSD 3-clause license: Copyright (C) 2010 Atsushi Togo All rights reserved. This file is part of spglib. https://github.com/atztogo/spglib Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of the phonopy project nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ #include #include #include "spg_database.hpp" #include "hall_symbol.hpp" using namespace brille; /* Modifications from spglib original: ' CENTERING_ERROR' --> 'Bravais::_' ' PRIMITIVE' --> 'Bravais::P' ' A_FACE' --> 'Bravais::A' ' B_FACE' --> 'Bravais::B' (not present) ' C_FACE' --> 'Bravais::C' ' BODY' --> 'Bravais::I' ' FACE' --> 'Bravais::F' ' R_CENTER' --> 'Bravais::R' ' BASE' --> 'Bravais::X' (not present) 2019-05-28 G Tucker */ /* The ALL_SPACEGROUP Spacegroup array has been switched from fixed-length char arrays to variable length const std::strings (once initialized) */ /* In Hall symbols (3rd column), the double-prime is an escaped double quote*/ static const Spacegroup ALL_SPACEGROUPS[] = { { 0, "" , "" , "" , "" , "" , "" , Bravais::_, 0, 0}, { 1, "C1^1" , "P 1" , "P 1" , "P 1" , "P1" , "" , Bravais::P, 1, 1}, { 2, "Ci^1" , "-P 1" , "P -1" , "P -1" , "P-1" , "" , Bravais::P, 2, 2}, { 3, "C2^1" , "P 2y" , "P 2 = P 1 2 1" , "P 1 2 1" , "P2" , "b" , Bravais::P, 3, 3}, { 3, "C2^1" , "P 2" , "P 2 = P 1 1 2" , "P 1 1 2" , "P2" , "c" , Bravais::P, 3, 4}, { 3, "C2^1" , "P 2x" , "P 2 = P 2 1 1" , "P 2 1 1" , "P2" , "a" , Bravais::P, 3, 5}, { 4, "C2^2" , "P 2yb" , "P 2_1 = P 1 2_1 1" , "P 1 2_1 1" , "P2_1" , "b" , Bravais::P, 3, 6}, { 4, "C2^2" , "P 2c" , "P 2_1 = P 1 1 2_1" , "P 1 1 2_1" , "P2_1" , "c" , Bravais::P, 3, 7}, { 4, "C2^2" , "P 2xa" , "P 2_1 = P 2_1 1 1" , "P 2_1 1 1" , "P2_1" , "a" , Bravais::P, 3, 8}, { 5, "C2^3" , "C 2y" , "C 2 = C 1 2 1" , "C 1 2 1" , "C2" , "b1" , Bravais::C, 3, 9}, { 5, "C2^3" , "A 2y" , "C 2 = A 1 2 1" , "A 1 2 1" , "C2" , "b2" , Bravais::A, 3, 10}, { 5, "C2^3" , "I 2y" , "C 2 = I 1 2 1" , "I 1 2 1" , "C2" , "b3" , Bravais::I, 3, 11}, { 5, "C2^3" , "A 2" , "C 2 = A 1 1 2" , "A 1 1 2" , "C2" , "c1" , Bravais::A, 3, 12}, { 5, "C2^3" , "B 2" , "C 2 = B 1 1 2 = B 2" , "B 1 1 2" , "C2" , "c2" , Bravais::P, 3, 13}, { 5, "C2^3" , "I 2" , "C 2 = I 1 1 2" , "I 1 1 2" , "C2" , "c3" , Bravais::I, 3, 14}, { 5, "C2^3" , "B 2x" , "C 2 = B 2 1 1" , "B 2 1 1" , "C2" , "a1" , Bravais::P, 3, 15}, { 5, "C2^3" , "C 2x" , "C 2 = C 2 1 1" , "C 2 1 1" , "C2" , "a2" , Bravais::C, 3, 16}, { 5, "C2^3" , "I 2x" , "C 2 = I 2 1 1" , "I 2 1 1" , "C2" , "a3" , Bravais::I, 3, 17}, { 6, "Cs^1" , "P -2y" , "P m = P 1 m 1" , "P 1 m 1" , "Pm" , "b" , Bravais::P, 4, 18}, { 6, "Cs^1" , "P -2" , "P m = P 1 1 m" , "P 1 1 m" , "Pm" , "c" , Bravais::P, 4, 19}, { 6, "Cs^1" , "P -2x" , "P m = P m 1 1" , "P m 1 1" , "Pm" , "a" , Bravais::P, 4, 20}, { 7, "Cs^2" , "P -2yc" , "P c = P 1 c 1" , "P 1 c 1" , "Pc" , "b1" , Bravais::P, 4, 21}, { 7, "Cs^2" , "P -2yac" , "P c = P 1 n 1" , "P 1 n 1" , "Pc" , "b2" , Bravais::P, 4, 22}, { 7, "Cs^2" , "P -2ya" , "P c = P 1 a 1" , "P 1 a 1" , "Pc" , "b3" , Bravais::P, 4, 23}, { 7, "Cs^2" , "P -2a" , "P c = P 1 1 a" , "P 1 1 a" , "Pc" , "c1" , Bravais::P, 4, 24}, { 7, "Cs^2" , "P -2ab" , "P c = P 1 1 n" , "P 1 1 n" , "Pc" , "c2" , Bravais::P, 4, 25}, { 7, "Cs^2" , "P -2b" , "P c = P 1 1 b = P b" , "P 1 1 b" , "Pc" , "c3" , Bravais::P, 4, 26}, { 7, "Cs^2" , "P -2xb" , "P c = P b 1 1" , "P b 1 1" , "Pc" , "a1" , Bravais::P, 4, 27}, { 7, "Cs^2" , "P -2xbc" , "P c = P n 1 1" , "P n 1 1" , "Pc" , "a2" , Bravais::P, 4, 28}, { 7, "Cs^2" , "P -2xc" , "P c = P c 1 1" , "P c 1 1" , "Pc" , "a3" , Bravais::P, 4, 29}, { 8, "Cs^3" , "C -2y" , "C m = C 1 m 1" , "C 1 m 1" , "Cm" , "b1" , Bravais::C, 4, 30}, { 8, "Cs^3" , "A -2y" , "C m = A 1 m 1" , "A 1 m 1" , "Cm" , "b2" , Bravais::A, 4, 31}, { 8, "Cs^3" , "I -2y" , "C m = I 1 m 1" , "I 1 m 1" , "Cm" , "b3" , Bravais::I, 4, 32}, { 8, "Cs^3" , "A -2" , "C m = A 1 1 m" , "A 1 1 m" , "Cm" , "c1" , Bravais::A, 4, 33}, { 8, "Cs^3" , "B -2" , "C m = B 1 1 m = B m" , "B 1 1 m" , "Cm" , "c2" , Bravais::P, 4, 34}, { 8, "Cs^3" , "I -2" , "C m = I 1 1 m" , "I 1 1 m" , "Cm" , "c3" , Bravais::I, 4, 35}, { 8, "Cs^3" , "B -2x" , "C m = B m 1 1" , "B m 1 1" , "Cm" , "a1" , Bravais::P, 4, 36}, { 8, "Cs^3" , "C -2x" , "C m = C m 1 1" , "C m 1 1" , "Cm" , "a2" , Bravais::C, 4, 37}, { 8, "Cs^3" , "I -2x" , "C m = I m 1 1" , "I m 1 1" , "Cm" , "a3" , Bravais::I, 4, 38}, { 9, "Cs^4" , "C -2yc" , "C c = C 1 c 1" , "C 1 c 1" , "Cc" , "b1" , Bravais::C, 4, 39}, { 9, "Cs^4" , "A -2yac" , "C c = A 1 n 1" , "A 1 n 1" , "Cc" , "b2" , Bravais::A, 4, 40}, { 9, "Cs^4" , "I -2ya" , "C c = I 1 a 1" , "I 1 a 1" , "Cc" , "b3" , Bravais::I, 4, 41}, { 9, "Cs^4" , "A -2ya" , "C c = A 1 a 1" , "A 1 a 1" , "Cc" , "-b1" , Bravais::A, 4, 42}, { 9, "Cs^4" , "C -2ybc" , "C c = C 1 n 1" , "C 1 n 1" , "Cc" , "-b2" , Bravais::C, 4, 43}, { 9, "Cs^4" , "I -2yc" , "C c = I 1 c 1" , "I 1 c 1" , "Cc" , "-b3" , Bravais::I, 4, 44}, { 9, "Cs^4" , "A -2a" , "C c = A 1 1 a" , "A 1 1 a" , "Cc" , "c1" , Bravais::A, 4, 45}, { 9, "Cs^4" , "B -2bc" , "C c = B 1 1 n" , "B 1 1 n" , "Cc" , "c2" , Bravais::P, 4, 46}, { 9, "Cs^4" , "I -2b" , "C c = I 1 1 b" , "I 1 1 b" , "Cc" , "c3" , Bravais::I, 4, 47}, { 9, "Cs^4" , "B -2b" , "C c = B 1 1 b = B b" , "B 1 1 b" , "Cc" , "-c1" , Bravais::P, 4, 48}, { 9, "Cs^4" , "A -2ac" , "C c = A 1 1 n" , "A 1 1 n" , "Cc" , "-c2" , Bravais::A, 4, 49}, { 9, "Cs^4" , "I -2a" , "C c = I 1 1 a" , "I 1 1 a" , "Cc" , "-c3" , Bravais::I, 4, 50}, { 9, "Cs^4" , "B -2xb" , "C c = B b 1 1" , "B b 1 1" , "Cc" , "a1" , Bravais::P, 4, 51}, { 9, "Cs^4" , "C -2xbc" , "C c = C n 1 1" , "C n 1 1" , "Cc" , "a2" , Bravais::C, 4, 52}, { 9, "Cs^4" , "I -2xc" , "C c = I c 1 1" , "I c 1 1" , "Cc" , "a3" , Bravais::I, 4, 53}, { 9, "Cs^4" , "C -2xc" , "C c = C c 1 1" , "C c 1 1" , "Cc" , "-a1" , Bravais::C, 4, 54}, { 9, "Cs^4" , "B -2xbc" , "C c = B n 1 1" , "B n 1 1" , "Cc" , "-a2" , Bravais::P, 4, 55}, { 9, "Cs^4" , "I -2xb" , "C c = I b 1 1" , "I b 1 1" , "Cc" , "-a3" , Bravais::I, 4, 56}, { 10, "C2h^1" , "-P 2y" , "P 2/m = P 1 2/m 1" , "P 1 2/m 1" , "P2/m" , "b" , Bravais::P, 5, 57}, { 10, "C2h^1" , "-P 2" , "P 2/m = P 1 1 2/m" , "P 1 1 2/m" , "P2/m" , "c" , Bravais::P, 5, 58}, { 10, "C2h^1" , "-P 2x" , "P 2/m = P 2/m 1 1" , "P 2/m 1 1" , "P2/m" , "a" , Bravais::P, 5, 59}, { 11, "C2h^2" , "-P 2yb" , "P 2_1/m = P 1 2_1/m 1" , "P 1 2_1/m 1" , "P2_1/m" , "b" , Bravais::P, 5, 60}, { 11, "C2h^2" , "-P 2c" , "P 2_1/m = P 1 1 2_1/m" , "P 1 1 2_1/m" , "P2_1/m" , "c" , Bravais::P, 5, 61}, { 11, "C2h^2" , "-P 2xa" , "P 2_1/m = P 2_1/m 1 1" , "P 2_1/m 1 1" , "P2_1/m" , "a" , Bravais::P, 5, 62}, { 12, "C2h^3" , "-C 2y" , "C 2/m = C 1 2/m 1" , "C 1 2/m 1" , "C2/m" , "b1" , Bravais::C, 5, 63}, { 12, "C2h^3" , "-A 2y" , "C 2/m = A 1 2/m 1" , "A 1 2/m 1" , "C2/m" , "b2" , Bravais::A, 5, 64}, { 12, "C2h^3" , "-I 2y" , "C 2/m = I 1 2/m 1" , "I 1 2/m 1" , "C2/m" , "b3" , Bravais::I, 5, 65}, { 12, "C2h^3" , "-A 2" , "C 2/m = A 1 1 2/m" , "A 1 1 2/m" , "C2/m" , "c1" , Bravais::A, 5, 66}, { 12, "C2h^3" , "-B 2" , "C 2/m = B 1 1 2/m = B 2/m" , "B 1 1 2/m" , "C2/m" , "c2" , Bravais::P, 5, 67}, { 12, "C2h^3" , "-I 2" , "C 2/m = I 1 1 2/m" , "I 1 1 2/m" , "C2/m" , "c3" , Bravais::I, 5, 68}, { 12, "C2h^3" , "-B 2x" , "C 2/m = B 2/m 1 1" , "B 2/m 1 1" , "C2/m" , "a1" , Bravais::P, 5, 69}, { 12, "C2h^3" , "-C 2x" , "C 2/m = C 2/m 1 1" , "C 2/m 1 1" , "C2/m" , "a2" , Bravais::C, 5, 70}, { 12, "C2h^3" , "-I 2x" , "C 2/m = I 2/m 1 1" , "I 2/m 1 1" , "C2/m" , "a3" , Bravais::I, 5, 71}, { 13, "C2h^4" , "-P 2yc" , "P 2/c = P 1 2/c 1" , "P 1 2/c 1" , "P2/c" , "b1" , Bravais::P, 5, 72}, { 13, "C2h^4" , "-P 2yac" , "P 2/c = P 1 2/n 1" , "P 1 2/n 1" , "P2/c" , "b2" , Bravais::P, 5, 73}, { 13, "C2h^4" , "-P 2ya" , "P 2/c = P 1 2/a 1" , "P 1 2/a 1" , "P2/c" , "b3" , Bravais::P, 5, 74}, { 13, "C2h^4" , "-P 2a" , "P 2/c = P 1 1 2/a" , "P 1 1 2/a" , "P2/c" , "c1" , Bravais::P, 5, 75}, { 13, "C2h^4" , "-P 2ab" , "P 2/c = P 1 1 2/n" , "P 1 1 2/n" , "P2/c" , "c2" , Bravais::P, 5, 76}, { 13, "C2h^4" , "-P 2b" , "P 2/c = P 1 1 2/b = P 2/b" , "P 1 1 2/b" , "P2/c" , "c3" , Bravais::P, 5, 77}, { 13, "C2h^4" , "-P 2xb" , "P 2/c = P 2/b 1 1" , "P 2/b 1 1" , "P2/c" , "a1" , Bravais::P, 5, 78}, { 13, "C2h^4" , "-P 2xbc" , "P 2/c = P 2/n 1 1" , "P 2/n 1 1" , "P2/c" , "a2" , Bravais::P, 5, 79}, { 13, "C2h^4" , "-P 2xc" , "P 2/c = P 2/c 1 1" , "P 2/c 1 1" , "P2/c" , "a3" , Bravais::P, 5, 80}, { 14, "C2h^5" , "-P 2ybc" , "P 2_1/c = P 1 2_1/c 1" , "P 1 2_1/c 1" , "P2_1/c" , "b1" , Bravais::P, 5, 81}, { 14, "C2h^5" , "-P 2yn" , "P 2_1/c = P 1 2_1/n 1" , "P 1 2_1/n 1" , "P2_1/c" , "b2" , Bravais::P, 5, 82}, { 14, "C2h^5" , "-P 2yab" , "P 2_1/c = P 1 2_1/a 1" , "P 1 2_1/a 1" , "P2_1/c" , "b3" , Bravais::P, 5, 83}, { 14, "C2h^5" , "-P 2ac" , "P 2_1/c = P 1 1 2_1/a" , "P 1 1 2_1/a" , "P2_1/c" , "c1" , Bravais::P, 5, 84}, { 14, "C2h^5" , "-P 2n" , "P 2_1/c = P 1 1 2_1/n" , "P 1 1 2_1/n" , "P2_1/c" , "c2" , Bravais::P, 5, 85}, { 14, "C2h^5" , "-P 2bc" , "P 2_1/c = P 1 1 2_1/b = P 2_1/b", "P 1 1 2_1/b" , "P2_1/c" , "c3" , Bravais::P, 5, 86}, { 14, "C2h^5" , "-P 2xab" , "P 2_1/c = P 2_1/b 1 1" , "P 2_1/b 1 1" , "P2_1/c" , "a1" , Bravais::P, 5, 87}, { 14, "C2h^5" , "-P 2xn" , "P 2_1/c = P 2_1/n 1 1" , "P 2_1/n 1 1" , "P2_1/c" , "a2" , Bravais::P, 5, 88}, { 14, "C2h^5" , "-P 2xac" , "P 2_1/c = P 2_1/c 1 1" , "P 2_1/c 1 1" , "P2_1/c" , "a3" , Bravais::P, 5, 89}, { 15, "C2h^6" , "-C 2yc" , "C 2/c = C 1 2/c 1" , "C 1 2/c 1" , "C2/c" , "b1" , Bravais::C, 5, 90}, { 15, "C2h^6" , "-A 2yac" , "C 2/c = A 1 2/n 1" , "A 1 2/n 1" , "C2/c" , "b2" , Bravais::A, 5, 91}, { 15, "C2h^6" , "-I 2ya" , "C 2/c = I 1 2/a 1" , "I 1 2/a 1" , "C2/c" , "b3" , Bravais::I, 5, 92}, { 15, "C2h^6" , "-A 2ya" , "C 2/c = A 1 2/a 1" , "A 1 2/a 1" , "C2/c" , "-b1" , Bravais::A, 5, 93}, { 15, "C2h^6" , "-C 2ybc" , "C 2/c = C 1 2/n 1" , "C 1 2/n 1" , "C2/c" , "-b2" , Bravais::C, 5, 94}, { 15, "C2h^6" , "-I 2yc" , "C 2/c = I 1 2/c 1" , "I 1 2/c 1" , "C2/c" , "-b3" , Bravais::I, 5, 95}, { 15, "C2h^6" , "-A 2a" , "C 2/c = A 1 1 2/a" , "A 1 1 2/a" , "C2/c" , "c1" , Bravais::A, 5, 96}, { 15, "C2h^6" , "-B 2bc" , "C 2/c = B 1 1 2/n" , "B 1 1 2/n" , "C2/c" , "c2" , Bravais::P, 5, 97}, { 15, "C2h^6" , "-I 2b" , "C 2/c = I 1 1 2/b" , "I 1 1 2/b" , "C2/c" , "c3" , Bravais::I, 5, 98}, { 15, "C2h^6" , "-B 2b" , "C 2/c = B 1 1 2/b = B 2/b" , "B 1 1 2/b" , "C2/c" , "-c1" , Bravais::P, 5, 99}, { 15, "C2h^6" , "-A 2ac" , "C 2/c = A 1 1 2/n" , "A 1 1 2/n" , "C2/c" , "-c2" , Bravais::A, 5, 100}, { 15, "C2h^6" , "-I 2a" , "C 2/c = I 1 1 2/a" , "I 1 1 2/a" , "C2/c" , "-c3" , Bravais::I, 5, 101}, { 15, "C2h^6" , "-B 2xb" , "C 2/c = B 2/b 1 1" , "B 2/b 1 1" , "C2/c" , "a1" , Bravais::P, 5, 102}, { 15, "C2h^6" , "-C 2xbc" , "C 2/c = C 2/n 1 1" , "C 2/n 1 1" , "C2/c" , "a2" , Bravais::C, 5, 103}, { 15, "C2h^6" , "-I 2xc" , "C 2/c = I 2/c 1 1" , "I 2/c 1 1" , "C2/c" , "a3" , Bravais::I, 5, 104}, { 15, "C2h^6" , "-C 2xc" , "C 2/c = C 2/c 1 1" , "C 2/c 1 1" , "C2/c" , "-a1" , Bravais::C, 5, 105}, { 15, "C2h^6" , "-B 2xbc" , "C 2/c = B 2/n 1 1" , "B 2/n 1 1" , "C2/c" , "-a2" , Bravais::P, 5, 106}, { 15, "C2h^6" , "-I 2xb" , "C 2/c = I 2/b 1 1" , "I 2/b 1 1" , "C2/c" , "-a3" , Bravais::I, 5, 107}, { 16, "D2^1" , "P 2 2" , "P 2 2 2" , "P 2 2 2" , "P222" , "" , Bravais::P, 6, 108}, { 17, "D2^2" , "P 2c 2" , "P 2 2 2_1" , "P 2 2 2_1" , "P222_1" , "" , Bravais::P, 6, 109}, { 17, "D2^2" , "P 2a 2a" , "P 2_1 2 2" , "P 2_1 2 2" , "P2_122" , "cab" , Bravais::P, 6, 110}, { 17, "D2^2" , "P 2 2b" , "P 2 2_1 2" , "P 2 2_1 2" , "P22_12" , "bca" , Bravais::P, 6, 111}, { 18, "D2^3" , "P 2 2ab" , "P 2_1 2_1 2" , "P 2_1 2_1 2" , "P2_12_12" , "" , Bravais::P, 6, 112}, { 18, "D2^3" , "P 2bc 2" , "P 2 2_1 2_1" , "P 2 2_1 2_1" , "P22_12_1" , "cab" , Bravais::P, 6, 113}, { 18, "D2^3" , "P 2ac 2ac" , "P 2_1 2 2_1" , "P 2_1 2 2_1" , "P2_122_1" , "bca" , Bravais::P, 6, 114}, { 19, "D2^4" , "P 2ac 2ab" , "P 2_1 2_1 2_1" , "P 2_1 2_1 2_1" , "P2_12_12_1", "" , Bravais::P, 6, 115}, { 20, "D2^5" , "C 2c 2" , "C 2 2 2_1" , "C 2 2 2_1" , "C222_1" , "" , Bravais::C, 6, 116}, { 20, "D2^5" , "A 2a 2a" , "A 2_1 2 2" , "A 2_1 2 2" , "A2_122" , "cab" , Bravais::A, 6, 117}, { 20, "D2^5" , "B 2 2b" , "B 2 2_1 2" , "B 2 2_1 2" , "B22_12" , "bca" , Bravais::P, 6, 118}, { 21, "D2^6" , "C 2 2" , "C 2 2 2" , "C 2 2 2" , "C222" , "" , Bravais::C, 6, 119}, { 21, "D2^6" , "A 2 2" , "A 2 2 2" , "A 2 2 2" , "A222" , "cab" , Bravais::A, 6, 120}, { 21, "D2^6" , "B 2 2" , "B 2 2 2" , "B 2 2 2" , "B222" , "bca" , Bravais::P, 6, 121}, { 22, "D2^7" , "F 2 2" , "F 2 2 2" , "F 2 2 2" , "F222" , "" , Bravais::F, 6, 122}, { 23, "D2^8" , "I 2 2" , "I 2 2 2" , "I 2 2 2" , "I222" , "" , Bravais::I, 6, 123}, { 24, "D2^9" , "I 2b 2c" , "I 2_1 2_1 2_1" , "I 2_1 2_1 2_1" , "I2_12_12_1", "" , Bravais::I, 6, 124}, { 25, "C2v^1" , "P 2 -2" , "P m m 2" , "P m m 2" , "Pmm2" , "" , Bravais::P, 7, 125}, { 25, "C2v^1" , "P -2 2" , "P 2 m m" , "P 2 m m" , "P2mm" , "cab" , Bravais::P, 7, 126}, { 25, "C2v^1" , "P -2 -2" , "P m 2 m" , "P m 2 m" , "Pm2m" , "bca" , Bravais::P, 7, 127}, { 26, "C2v^2" , "P 2c -2" , "P m c 2_1" , "P m c 2_1" , "Pmc2_1" , "" , Bravais::P, 7, 128}, { 26, "C2v^2" , "P 2c -2c" , "P c m 2_1" , "P c m 2_1" , "Pcm2_1" , "ba-c" , Bravais::P, 7, 129}, { 26, "C2v^2" , "P -2a 2a" , "P 2_1 m a" , "P 2_1 m a" , "P2_1ma" , "cab" , Bravais::P, 7, 130}, { 26, "C2v^2" , "P -2 2a" , "P 2_1 a m" , "P 2_1 a m" , "P2_1am" , "-cba" , Bravais::P, 7, 131}, { 26, "C2v^2" , "P -2 -2b" , "P b 2_1 m" , "P b 2_1 m" , "Pb2_1m" , "bca" , Bravais::P, 7, 132}, { 26, "C2v^2" , "P -2b -2" , "P m 2_1 b" , "P m 2_1 b" , "Pm2_1b" , "a-cb" , Bravais::P, 7, 133}, { 27, "C2v^3" , "P 2 -2c" , "P c c 2" , "P c c 2" , "Pcc2" , "" , Bravais::P, 7, 134}, { 27, "C2v^3" , "P -2a 2" , "P 2 a a" , "P 2 a a" , "P2aa" , "cab" , Bravais::P, 7, 135}, { 27, "C2v^3" , "P -2b -2b" , "P b 2 b" , "P b 2 b" , "Pb2b" , "bca" , Bravais::P, 7, 136}, { 28, "C2v^4" , "P 2 -2a" , "P m a 2" , "P m a 2" , "Pma2" , "" , Bravais::P, 7, 137}, { 28, "C2v^4" , "P 2 -2b" , "P b m 2" , "P b m 2" , "Pbm2" , "ba-c" , Bravais::P, 7, 138}, { 28, "C2v^4" , "P -2b 2" , "P 2 m b" , "P 2 m b" , "P2mb" , "cab" , Bravais::P, 7, 139}, { 28, "C2v^4" , "P -2c 2" , "P 2 c m" , "P 2 c m" , "P2cm" , "-cba" , Bravais::P, 7, 140}, { 28, "C2v^4" , "P -2c -2c" , "P c 2 m" , "P c 2 m" , "Pc2m" , "bca" , Bravais::P, 7, 141}, { 28, "C2v^4" , "P -2a -2a" , "P m 2 a" , "P m 2 a" , "Pm2a" , "a-cb" , Bravais::P, 7, 142}, { 29, "C2v^5" , "P 2c -2ac" , "P c a 2_1" , "P c a 2_1" , "Pca2_1" , "" , Bravais::P, 7, 143}, { 29, "C2v^5" , "P 2c -2b" , "P b c 2_1" , "P b c 2_1" , "Pbc2_1" , "ba-c" , Bravais::P, 7, 144}, { 29, "C2v^5" , "P -2b 2a" , "P 2_1 a b" , "P 2_1 a b" , "P2_1ab" , "cab" , Bravais::P, 7, 145}, { 29, "C2v^5" , "P -2ac 2a" , "P 2_1 c a" , "P 2_1 c a" , "P2_1ca" , "-cba" , Bravais::P, 7, 146}, { 29, "C2v^5" , "P -2bc -2c" , "P c 2_1 b" , "P c 2_1 b" , "Pc2_1b" , "bca" , Bravais::P, 7, 147}, { 29, "C2v^5" , "P -2a -2ab" , "P b 2_1 a" , "P b 2_1 a" , "Pb2_1a" , "a-cb" , Bravais::P, 7, 148}, { 30, "C2v^6" , "P 2 -2bc" , "P n c 2" , "P n c 2" , "Pnc2" , "" , Bravais::P, 7, 149}, { 30, "C2v^6" , "P 2 -2ac" , "P c n 2" , "P c n 2" , "Pcn2" , "ba-c" , Bravais::P, 7, 150}, { 30, "C2v^6" , "P -2ac 2" , "P 2 n a" , "P 2 n a" , "P2na" , "cab" , Bravais::P, 7, 151}, { 30, "C2v^6" , "P -2ab 2" , "P 2 a n" , "P 2 a n" , "P2an" , "-cba" , Bravais::P, 7, 152}, { 30, "C2v^6" , "P -2ab -2ab" , "P b 2 n" , "P b 2 n" , "Pb2n" , "bca" , Bravais::P, 7, 153}, { 30, "C2v^6" , "P -2bc -2bc" , "P n 2 b" , "P n 2 b" , "Pn2b" , "a-cb" , Bravais::P, 7, 154}, { 31, "C2v^7" , "P 2ac -2" , "P m n 2_1" , "P m n 2_1" , "Pmn2_1" , "" , Bravais::P, 7, 155}, { 31, "C2v^7" , "P 2bc -2bc" , "P n m 2_1" , "P n m 2_1" , "Pnm2_1" , "ba-c" , Bravais::P, 7, 156}, { 31, "C2v^7" , "P -2ab 2ab" , "P 2_1 m n" , "P 2_1 m n" , "P2_1mn" , "cab" , Bravais::P, 7, 157}, { 31, "C2v^7" , "P -2 2ac" , "P 2_1 n m" , "P 2_1 n m" , "P2_1nm" , "-cba" , Bravais::P, 7, 158}, { 31, "C2v^7" , "P -2 -2bc" , "P n 2_1 m" , "P n 2_1 m" , "Pn2_1m" , "bca" , Bravais::P, 7, 159}, { 31, "C2v^7" , "P -2ab -2" , "P m 2_1 n" , "P m 2_1 n" , "Pm2_1n" , "a-cb" , Bravais::P, 7, 160}, { 32, "C2v^8" , "P 2 -2ab" , "P b a 2" , "P b a 2" , "Pba2" , "" , Bravais::P, 7, 161}, { 32, "C2v^8" , "P -2bc 2" , "P 2 c b" , "P 2 c b" , "P2cb" , "cab" , Bravais::P, 7, 162}, { 32, "C2v^8" , "P -2ac -2ac" , "P c 2 a" , "P c 2 a" , "Pc2a" , "bca" , Bravais::P, 7, 163}, { 33, "C2v^9" , "P 2c -2n" , "P n a 2_1" , "P n a 2_1" , "Pna2_1" , "" , Bravais::P, 7, 164}, { 33, "C2v^9" , "P 2c -2ab" , "P b n 2_1" , "P b n 2_1" , "Pbn2_1" , "ba-c" , Bravais::P, 7, 165}, { 33, "C2v^9" , "P -2bc 2a" , "P 2_1 n b" , "P 2_1 n b" , "P2_1nb" , "cab" , Bravais::P, 7, 166}, { 33, "C2v^9" , "P -2n 2a" , "P 2_1 c n" , "P 2_1 c n" , "P2_1cn" , "-cba" , Bravais::P, 7, 167}, { 33, "C2v^9" , "P -2n -2ac" , "P c 2_1 n" , "P c 2_1 n" , "Pc2_1n" , "bca" , Bravais::P, 7, 168}, { 33, "C2v^9" , "P -2ac -2n" , "P n 2_1 a" , "P n 2_1 a" , "Pn2_1a" , "a-cb" , Bravais::P, 7, 169}, { 34, "C2v^10", "P 2 -2n" , "P n n 2" , "P n n 2" , "Pnn2" , "" , Bravais::P, 7, 170}, { 34, "C2v^10", "P -2n 2" , "P 2 n n" , "P 2 n n" , "P2nn" , "cab" , Bravais::P, 7, 171}, { 34, "C2v^10", "P -2n -2n" , "P n 2 n" , "P n 2 n" , "Pn2n" , "bca" , Bravais::P, 7, 172}, { 35, "C2v^11", "C 2 -2" , "C m m 2" , "C m m 2" , "Cmm2" , "" , Bravais::C, 7, 173}, { 35, "C2v^11", "A -2 2" , "A 2 m m" , "A 2 m m" , "A2mm" , "cab" , Bravais::A, 7, 174}, { 35, "C2v^11", "B -2 -2" , "B m 2 m" , "B m 2 m" , "Bm2m" , "bca" , Bravais::P, 7, 175}, { 36, "C2v^12", "C 2c -2" , "C m c 2_1" , "C m c 2_1" , "Cmc2_1" , "" , Bravais::C, 7, 176}, { 36, "C2v^12", "C 2c -2c" , "C c m 2_1" , "C c m 2_1" , "Ccm2_1" , "ba-c" , Bravais::C, 7, 177}, { 36, "C2v^12", "A -2a 2a" , "A 2_1 m a" , "A 2_1 m a" , "A2_1ma" , "cab" , Bravais::A, 7, 178}, { 36, "C2v^12", "A -2 2a" , "A 2_1 a m" , "A 2_1 a m" , "A2_1am" , "-cba" , Bravais::A, 7, 179}, { 36, "C2v^12", "B -2 -2b" , "B b 2_1 m" , "B b 2_1 m" , "Bb2_1m" , "bca" , Bravais::P, 7, 180}, { 36, "C2v^12", "B -2b -2" , "B m 2_1 b" , "B m 2_1 b" , "Bm2_1b" , "a-cb" , Bravais::P, 7, 181}, { 37, "C2v^13", "C 2 -2c" , "C c c 2" , "C c c 2" , "Ccc2" , "" , Bravais::C, 7, 182}, { 37, "C2v^13", "A -2a 2" , "A 2 a a" , "A 2 a a" , "A2aa" , "cab" , Bravais::A, 7, 183}, { 37, "C2v^13", "B -2b -2b" , "B b 2 b" , "B b 2 b" , "Bb2b" , "bca" , Bravais::P, 7, 184}, { 38, "C2v^14", "A 2 -2" , "A m m 2" , "A m m 2" , "Amm2" , "" , Bravais::A, 7, 185}, { 38, "C2v^14", "B 2 -2" , "B m m 2" , "B m m 2" , "Bmm2" , "ba-c" , Bravais::P, 7, 186}, { 38, "C2v^14", "B -2 2" , "B 2 m m" , "B 2 m m" , "B2mm" , "cab" , Bravais::P, 7, 187}, { 38, "C2v^14", "C -2 2" , "C 2 m m" , "C 2 m m" , "C2mm" , "-cba" , Bravais::C, 7, 188}, { 38, "C2v^14", "C -2 -2" , "C m 2 m" , "C m 2 m" , "Cm2m" , "bca" , Bravais::C, 7, 189}, { 38, "C2v^14", "A -2 -2" , "A m 2 m" , "A m 2 m" , "Am2m" , "a-cb" , Bravais::A, 7, 190}, { 39, "C2v^15", "A 2 -2c" , "A e m 2" , "A e m 2" , "Aem2" , "" , Bravais::A, 7, 191}, { 39, "C2v^15", "B 2 -2c" , "B m e 2" , "B m e 2" , "Bme2" , "ba-c" , Bravais::P, 7, 192}, { 39, "C2v^15", "B -2c 2" , "B 2 e m" , "B 2 e m" , "B2em" , "cab" , Bravais::P, 7, 193}, { 39, "C2v^15", "C -2b 2" , "C 2 m e" , "C 2 m e" , "C2me" , "-cba" , Bravais::C, 7, 194}, { 39, "C2v^15", "C -2b -2b" , "C m 2 e" , "C m 2 e" , "Cm2e" , "bca" , Bravais::C, 7, 195}, { 39, "C2v^15", "A -2c -2c" , "A e 2 m" , "A e 2 m" , "Ae2m" , "a-cb" , Bravais::A, 7, 196}, { 40, "C2v^16", "A 2 -2a" , "A m a 2" , "A m a 2" , "Ama2" , "" , Bravais::A, 7, 197}, { 40, "C2v^16", "B 2 -2b" , "B b m 2" , "B b m 2" , "Bbm2" , "ba-c" , Bravais::P, 7, 198}, { 40, "C2v^16", "B -2b 2" , "B 2 m b" , "B 2 m b" , "B2mb" , "cab" , Bravais::P, 7, 199}, { 40, "C2v^16", "C -2c 2" , "C 2 c m" , "C 2 c m" , "C2cm" , "-cba" , Bravais::C, 7, 200}, { 40, "C2v^16", "C -2c -2c" , "C c 2 m" , "C c 2 m" , "Cc2m" , "bca" , Bravais::C, 7, 201}, { 40, "C2v^16", "A -2a -2a" , "A m 2 a" , "A m 2 a" , "Am2a" , "a-cb" , Bravais::A, 7, 202}, { 41, "C2v^17", "A 2 -2ac" , "A e a 2" , "A e a 2" , "Aea2" , "" , Bravais::A, 7, 203}, { 41, "C2v^17", "B 2 -2bc" , "B b e 2" , "B b e 2" , "Bbe2" , "ba-c" , Bravais::P, 7, 204}, { 41, "C2v^17", "B -2bc 2" , "B 2 e b" , "B 2 e b" , "B2eb" , "cab" , Bravais::P, 7, 205}, { 41, "C2v^17", "C -2bc 2" , "C 2 c e" , "C 2 c e" , "C2ce" , "-cba" , Bravais::C, 7, 206}, { 41, "C2v^17", "C -2bc -2bc" , "C c 2 e" , "C c 2 e" , "Cc2e" , "bca" , Bravais::C, 7, 207}, { 41, "C2v^17", "A -2ac -2ac" , "A e 2 a" , "A e 2 a" , "Ae2a" , "a-cb" , Bravais::A, 7, 208}, { 42, "C2v^18", "F 2 -2" , "F m m 2" , "F m m 2" , "Fmm2" , "" , Bravais::F, 7, 209}, { 42, "C2v^18", "F -2 2" , "F 2 m m" , "F 2 m m" , "F2mm" , "cab" , Bravais::F, 7, 210}, { 42, "C2v^18", "F -2 -2" , "F m 2 m" , "F m 2 m" , "Fm2m" , "bca" , Bravais::F, 7, 211}, { 43, "C2v^19", "F 2 -2d" , "F d d 2" , "F d d 2" , "Fdd2" , "" , Bravais::F, 7, 212}, { 43, "C2v^19", "F -2d 2" , "F 2 d d" , "F 2 d d" , "F2dd" , "cab" , Bravais::F, 7, 213}, { 43, "C2v^19", "F -2d -2d" , "F d 2 d" , "F d 2 d" , "Fd2d" , "bca" , Bravais::F, 7, 214}, { 44, "C2v^20", "I 2 -2" , "I m m 2" , "I m m 2" , "Imm2" , "" , Bravais::I, 7, 215}, { 44, "C2v^20", "I -2 2" , "I 2 m m" , "I 2 m m" , "I2mm" , "cab" , Bravais::I, 7, 216}, { 44, "C2v^20", "I -2 -2" , "I m 2 m" , "I m 2 m" , "Im2m" , "bca" , Bravais::I, 7, 217}, { 45, "C2v^21", "I 2 -2c" , "I b a 2" , "I b a 2" , "Iba2" , "" , Bravais::I, 7, 218}, { 45, "C2v^21", "I -2a 2" , "I 2 c b" , "I 2 c b" , "I2cb" , "cab" , Bravais::I, 7, 219}, { 45, "C2v^21", "I -2b -2b" , "I c 2 a" , "I c 2 a" , "Ic2a" , "bca" , Bravais::I, 7, 220}, { 46, "C2v^22", "I 2 -2a" , "I m a 2" , "I m a 2" , "Ima2" , "" , Bravais::I, 7, 221}, { 46, "C2v^22", "I 2 -2b" , "I b m 2" , "I b m 2" , "Ibm2" , "ba-c" , Bravais::I, 7, 222}, { 46, "C2v^22", "I -2b 2" , "I 2 m b" , "I 2 m b" , "I2mb" , "cab" , Bravais::I, 7, 223}, { 46, "C2v^22", "I -2c 2" , "I 2 c m" , "I 2 c m" , "I2cm" , "-cba" , Bravais::I, 7, 224}, { 46, "C2v^22", "I -2c -2c" , "I c 2 m" , "I c 2 m" , "Ic2m" , "bca" , Bravais::I, 7, 225}, { 46, "C2v^22", "I -2a -2a" , "I m 2 a" , "I m 2 a" , "Im2a" , "a-cb" , Bravais::I, 7, 226}, { 47, "D2h^1" , "-P 2 2" , "P m m m" , "P 2/m 2/m 2/m" , "Pmmm" , "" , Bravais::P, 8, 227}, { 48, "D2h^2" , "P 2 2 -1n" , "P n n n" , "P 2/n 2/n 2/n" , "Pnnn" , "1" , Bravais::P, 8, 228}, { 48, "D2h^2" , "-P 2ab 2bc" , "P n n n" , "P 2/n 2/n 2/n" , "Pnnn" , "2" , Bravais::P, 8, 229}, { 49, "D2h^3" , "-P 2 2c" , "P c c m" , "P 2/c 2/c 2/m" , "Pccm" , "" , Bravais::P, 8, 230}, { 49, "D2h^3" , "-P 2a 2" , "P m a a" , "P 2/m 2/a 2/a" , "Pmaa" , "cab" , Bravais::P, 8, 231}, { 49, "D2h^3" , "-P 2b 2b" , "P b m b" , "P 2/b 2/m 2/b" , "Pbmb" , "bca" , Bravais::P, 8, 232}, { 50, "D2h^4" , "P 2 2 -1ab" , "P b a n" , "P 2/b 2/a 2/n" , "Pban" , "1" , Bravais::P, 8, 233}, { 50, "D2h^4" , "-P 2ab 2b" , "P b a n" , "P 2/b 2/a 2/n" , "Pban" , "2" , Bravais::P, 8, 234}, { 50, "D2h^4" , "P 2 2 -1bc" , "P n c b" , "P 2/n 2/c 2/b" , "Pncb" , "1cab" , Bravais::P, 8, 235}, { 50, "D2h^4" , "-P 2b 2bc" , "P n c b" , "P 2/n 2/c 2/b" , "Pncb" , "2cab" , Bravais::P, 8, 236}, { 50, "D2h^4" , "P 2 2 -1ac" , "P c n a" , "P 2/c 2/n 2/a" , "Pcna" , "1bca" , Bravais::P, 8, 237}, { 50, "D2h^4" , "-P 2a 2c" , "P c n a" , "P 2/c 2/n 2/a" , "Pcna" , "2bca" , Bravais::P, 8, 238}, { 51, "D2h^5" , "-P 2a 2a" , "P m m a" , "P 2_1/m 2/m 2/a" , "Pmma" , "" , Bravais::P, 8, 239}, { 51, "D2h^5" , "-P 2b 2" , "P m m b" , "P 2/m 2_1/m 2/b" , "Pmmb" , "ba-c" , Bravais::P, 8, 240}, { 51, "D2h^5" , "-P 2 2b" , "P b m m" , "P 2/b 2_1/m 2/m" , "Pbmm" , "cab" , Bravais::P, 8, 241}, { 51, "D2h^5" , "-P 2c 2c" , "P c m m" , "P 2/c 2/m 2_1/m" , "Pcmm" , "-cba" , Bravais::P, 8, 242}, { 51, "D2h^5" , "-P 2c 2" , "P m c m" , "P 2/m 2/c 2_1/m" , "Pmcm" , "bca" , Bravais::P, 8, 243}, { 51, "D2h^5" , "-P 2 2a" , "P m a m" , "P 2_1/m 2/a 2/m" , "Pmam" , "a-cb" , Bravais::P, 8, 244}, { 52, "D2h^6" , "-P 2a 2bc" , "P n n a" , "P 2/n 2_1/n 2/a" , "Pnna" , "" , Bravais::P, 8, 245}, { 52, "D2h^6" , "-P 2b 2n" , "P n n b" , "P 2_1/n 2/n 2/b" , "Pnnb" , "ba-c" , Bravais::P, 8, 246}, { 52, "D2h^6" , "-P 2n 2b" , "P b n n" , "P 2/b 2/n 2_1/n" , "Pbnn" , "cab" , Bravais::P, 8, 247}, { 52, "D2h^6" , "-P 2ab 2c" , "P c n n" , "P 2/c 2_1/n 2/n" , "Pcnn" , "-cba" , Bravais::P, 8, 248}, { 52, "D2h^6" , "-P 2ab 2n" , "P n c n" , "P 2_1/n 2/c 2/n" , "Pncn" , "bca" , Bravais::P, 8, 249}, { 52, "D2h^6" , "-P 2n 2bc" , "P n a n" , "P 2/n 2/a 2_1/n" , "Pnan" , "a-cb" , Bravais::P, 8, 250}, { 53, "D2h^7" , "-P 2ac 2" , "P m n a" , "P 2/m 2/n 2_1/a" , "Pmna" , "" , Bravais::P, 8, 251}, { 53, "D2h^7" , "-P 2bc 2bc" , "P n m b" , "P 2/n 2/m 2_1/b" , "Pnmb" , "ba-c" , Bravais::P, 8, 252}, { 53, "D2h^7" , "-P 2ab 2ab" , "P b m n" , "P 2_1/b 2/m 2/n" , "Pbmn" , "cab" , Bravais::P, 8, 253}, { 53, "D2h^7" , "-P 2 2ac" , "P c n m" , "P 2_1/c 2/n 2/m" , "Pcnm" , "-cba" , Bravais::P, 8, 254}, { 53, "D2h^7" , "-P 2 2bc" , "P n c m" , "P 2/n 2_1/c 2/m" , "Pncm" , "bca" , Bravais::P, 8, 255}, { 53, "D2h^7" , "-P 2ab 2" , "P m a n" , "P 2/m 2_1/a 2/n" , "Pman" , "a-cb" , Bravais::P, 8, 256}, { 54, "D2h^8" , "-P 2a 2ac" , "P c c a" , "P 2_1/c 2/c 2/a" , "Pcca" , "" , Bravais::P, 8, 257}, { 54, "D2h^8" , "-P 2b 2c" , "P c c b" , "P 2/c 2_1/c 2/b" , "Pccb" , "ba-c" , Bravais::P, 8, 258}, { 54, "D2h^8" , "-P 2a 2b" , "P b a a" , "P 2/b 2_1/a 2/a" , "Pbaa" , "cab" , Bravais::P, 8, 259}, { 54, "D2h^8" , "-P 2ac 2c" , "P c a a" , "P 2/c 2/a 2_1/a" , "Pcaa" , "-cba" , Bravais::P, 8, 260}, { 54, "D2h^8" , "-P 2bc 2b" , "P b c b" , "P 2/b 2/c 2_1/b" , "Pbcb" , "bca" , Bravais::P, 8, 261}, { 54, "D2h^8" , "-P 2b 2ab" , "P b a b" , "P 2_1/b 2/a 2/b" , "Pbab" , "a-cb" , Bravais::P, 8, 262}, { 55, "D2h^9" , "-P 2 2ab" , "P b a m" , "P 2_1/b 2_1/a 2/m" , "Pbam" , "" , Bravais::P, 8, 263}, { 55, "D2h^9" , "-P 2bc 2" , "P m c b" , "P 2/m 2_1/c 2_1/b" , "Pmcb" , "cab" , Bravais::P, 8, 264}, { 55, "D2h^9" , "-P 2ac 2ac" , "P c m a" , "P 2_1/c 2/m 2_1/a" , "Pcma" , "bca" , Bravais::P, 8, 265}, { 56, "D2h^10", "-P 2ab 2ac" , "P c c n" , "P 2_1/c 2_1/c 2/n" , "Pccn" , "" , Bravais::P, 8, 266}, { 56, "D2h^10", "-P 2ac 2bc" , "P n a a" , "P 2/n 2_1/a 2_1/a" , "Pnaa" , "cab" , Bravais::P, 8, 267}, { 56, "D2h^10", "-P 2bc 2ab" , "P b n b" , "P 2_1/b 2/n 2_1/b" , "Pbnb" , "bca" , Bravais::P, 8, 268}, { 57, "D2h^11", "-P 2c 2b" , "P b c m" , "P 2/b 2_1/c 2_1/m" , "Pbcm" , "" , Bravais::P, 8, 269}, { 57, "D2h^11", "-P 2c 2ac" , "P c a m" , "P 2_1/c 2/a 2_1/m" , "Pcam" , "ba-c" , Bravais::P, 8, 270}, { 57, "D2h^11", "-P 2ac 2a" , "P m c a" , "P 2_1/m 2/c 2_1/a" , "Pmca" , "cab" , Bravais::P, 8, 271}, { 57, "D2h^11", "-P 2b 2a" , "P m a b" , "P 2_1/m 2_1/a 2/b" , "Pmab" , "-cba" , Bravais::P, 8, 272}, { 57, "D2h^11", "-P 2a 2ab" , "P b m a" , "P 2_1/b 2_1/m 2/a" , "Pbma" , "bca" , Bravais::P, 8, 273}, { 57, "D2h^11", "-P 2bc 2c" , "P c m b" , "P 2/c 2_1/m 2_1/b" , "Pcmb" , "a-cb" , Bravais::P, 8, 274}, { 58, "D2h^12", "-P 2 2n" , "P n n m" , "P 2_1/n 2_1/n 2/m" , "Pnnm" , "" , Bravais::P, 8, 275}, { 58, "D2h^12", "-P 2n 2" , "P m n n" , "P 2/m 2_1/n 2_1/n" , "Pmnn" , "cab" , Bravais::P, 8, 276}, { 58, "D2h^12", "-P 2n 2n" , "P n m n" , "P 2_1/n 2/m 2_1/n" , "Pnmn" , "bca" , Bravais::P, 8, 277}, { 59, "D2h^13", "P 2 2ab -1ab" , "P m m n" , "P 2_1/m 2_1/m 2/n" , "Pmmn" , "1" , Bravais::P, 8, 278}, { 59, "D2h^13", "-P 2ab 2a" , "P m m n" , "P 2_1/m 2_1/m 2/n" , "Pmmn" , "2" , Bravais::P, 8, 279}, { 59, "D2h^13", "P 2bc 2 -1bc" , "P n m m" , "P 2/n 2_1/m 2_1/m" , "Pnmm" , "1cab" , Bravais::P, 8, 280}, { 59, "D2h^13", "-P 2c 2bc" , "P n m m" , "P 2/n 2_1/m 2_1/m" , "Pnmm" , "2cab" , Bravais::P, 8, 281}, { 59, "D2h^13", "P 2ac 2ac -1ac" , "P m n m" , "P 2_1/m 2/n 2_1/m" , "Pmnm" , "1bca" , Bravais::P, 8, 282}, { 59, "D2h^13", "-P 2c 2a" , "P m n m" , "P 2_1/m 2/n 2_1/m" , "Pmnm" , "2bca" , Bravais::P, 8, 283}, { 60, "D2h^14", "-P 2n 2ab" , "P b c n" , "P 2_1/b 2/c 2_1/n" , "Pbcn" , "" , Bravais::P, 8, 284}, { 60, "D2h^14", "-P 2n 2c" , "P c a n" , "P 2/c 2_1/a 2_1/n" , "Pcan" , "ba-c" , Bravais::P, 8, 285}, { 60, "D2h^14", "-P 2a 2n" , "P n c a" , "P 2_1/n 2_1/c 2/a" , "Pnca" , "cab" , Bravais::P, 8, 286}, { 60, "D2h^14", "-P 2bc 2n" , "P n a b" , "P 2_1/n 2/a 2_1/b" , "Pnab" , "-cba" , Bravais::P, 8, 287}, { 60, "D2h^14", "-P 2ac 2b" , "P b n a" , "P 2/b 2_1/n 2_1/a" , "Pbna" , "bca" , Bravais::P, 8, 288}, { 60, "D2h^14", "-P 2b 2ac" , "P c n b" , "P 2_1/c 2_1/n 2/b" , "Pcnb" , "a-cb" , Bravais::P, 8, 289}, { 61, "D2h^15", "-P 2ac 2ab" , "P b c a" , "P 2_1/b 2_1/c 2_1/a", "Pbca" , "" , Bravais::P, 8, 290}, { 61, "D2h^15", "-P 2bc 2ac" , "P c a b" , "P 2_1/c 2_1/a 2_1/b", "Pcab" , "ba-c" , Bravais::P, 8, 291}, { 62, "D2h^16", "-P 2ac 2n" , "P n m a" , "P 2_1/n 2_1/m 2_1/a", "Pnma" , "" , Bravais::P, 8, 292}, { 62, "D2h^16", "-P 2bc 2a" , "P m n b" , "P 2_1/m 2_1/n 2_1/b", "Pmnb" , "ba-c" , Bravais::P, 8, 293}, { 62, "D2h^16", "-P 2c 2ab" , "P b n m" , "P 2_1/b 2_1/n 2_1/m", "Pbnm" , "cab" , Bravais::P, 8, 294}, { 62, "D2h^16", "-P 2n 2ac" , "P c m n" , "P 2_1/c 2_1/m 2_1/n", "Pcmn" , "-cba" , Bravais::P, 8, 295}, { 62, "D2h^16", "-P 2n 2a" , "P m c n" , "P 2_1/m 2_1/c 2_1/n", "Pmcn" , "bca" , Bravais::P, 8, 296}, { 62, "D2h^16", "-P 2c 2n" , "P n a m" , "P 2_1/n 2_1/a 2_1/m", "Pnam" , "a-cb" , Bravais::P, 8, 297}, { 63, "D2h^17", "-C 2c 2" , "C m c m" , "C 2/m 2/c 2_1/m" , "Cmcm" , "" , Bravais::C, 8, 298}, { 63, "D2h^17", "-C 2c 2c" , "C c m m" , "C 2/c 2/m 2_1/m" , "Ccmm" , "ba-c" , Bravais::C, 8, 299}, { 63, "D2h^17", "-A 2a 2a" , "A m m a" , "A 2_1/m 2/m 2/a" , "Amma" , "cab" , Bravais::A, 8, 300}, { 63, "D2h^17", "-A 2 2a" , "A m a m" , "A 2_1/m 2/a 2/m" , "Amam" , "-cba" , Bravais::A, 8, 301}, { 63, "D2h^17", "-B 2 2b" , "B b m m" , "B 2/b 2_1/m 2/m" , "Bbmm" , "bca" , Bravais::P, 8, 302}, { 63, "D2h^17", "-B 2b 2" , "B m m b" , "B 2/m 2_1/m 2/b" , "Bmmb" , "a-cb" , Bravais::P, 8, 303}, { 64, "D2h^18", "-C 2bc 2" , "C m c e" , "C 2/m 2/c 2_1/e" , "Cmce" , "" , Bravais::C, 8, 304}, { 64, "D2h^18", "-C 2bc 2bc" , "C c m e" , "C 2/c 2/m 2_1/e" , "Ccme" , "ba-c" , Bravais::C, 8, 305}, { 64, "D2h^18", "-A 2ac 2ac" , "A e m a" , "A 2_1/e 2/m 2/a" , "Aema" , "cab" , Bravais::A, 8, 306}, { 64, "D2h^18", "-A 2 2ac" , "A e a m" , "A 2_1/e 2/a 2/m" , "Aeam" , "-cba" , Bravais::A, 8, 307}, { 64, "D2h^18", "-B 2 2bc" , "B b e m" , "B 2/b 2_1/e 2/m" , "Bbem" , "bca" , Bravais::P, 8, 308}, { 64, "D2h^18", "-B 2bc 2" , "B m e b" , "B 2/m 2_1/e 2/b" , "Bmeb" , "a-cb" , Bravais::P, 8, 309}, { 65, "D2h^19", "-C 2 2" , "C m m m" , "C 2/m 2/m 2/m" , "Cmmm" , "" , Bravais::C, 8, 310}, { 65, "D2h^19", "-A 2 2" , "A m m m" , "A 2/m 2/m 2/m" , "Ammm" , "cab" , Bravais::A, 8, 311}, { 65, "D2h^19", "-B 2 2" , "B m m m" , "B 2/m 2/m 2/m" , "Bmmm" , "bca" , Bravais::P, 8, 312}, { 66, "D2h^20", "-C 2 2c" , "C c c m" , "C 2/c 2/c 2/m" , "Cccm" , "" , Bravais::C, 8, 313}, { 66, "D2h^20", "-A 2a 2" , "A m a a" , "A 2/m 2/a 2/a" , "Amaa" , "cab" , Bravais::A, 8, 314}, { 66, "D2h^20", "-B 2b 2b" , "B b m b" , "B 2/b 2/m 2/b" , "Bbmb" , "bca" , Bravais::P, 8, 315}, { 67, "D2h^21", "-C 2b 2" , "C m m e" , "C 2/m 2/m 2/e" , "Cmme" , "" , Bravais::C, 8, 316}, { 67, "D2h^21", "-C 2b 2b" , "C m m e" , "C 2/m 2/m 2/e" , "Cmme" , "ba-c" , Bravais::C, 8, 317}, { 67, "D2h^21", "-A 2c 2c" , "A e m m" , "A 2/e 2/m 2/m" , "Aemm" , "cab" , Bravais::A, 8, 318}, { 67, "D2h^21", "-A 2 2c" , "A e m m" , "A 2/e 2/m 2/m" , "Aemm" , "-cba" , Bravais::A, 8, 319}, { 67, "D2h^21", "-B 2 2c" , "B m e m" , "B 2/m 2/e 2/m" , "Bmem" , "bca" , Bravais::P, 8, 320}, { 67, "D2h^21", "-B 2c 2" , "B m e m" , "B 2/m 2/e 2/m" , "Bmem" , "a-cb" , Bravais::P, 8, 321}, { 68, "D2h^22", "C 2 2 -1bc" , "C c c e" , "C 2/c 2/c 2/e" , "Ccce" , "1" , Bravais::C, 8, 322}, { 68, "D2h^22", "-C 2b 2bc" , "C c c e" , "C 2/c 2/c 2/e" , "Ccce" , "2" , Bravais::C, 8, 323}, { 68, "D2h^22", "C 2 2 -1bc" , "C c c e" , "C 2/c 2/c 2/e" , "Ccce" , "1ba-c", Bravais::C, 8, 324}, { 68, "D2h^22", "-C 2b 2c" , "C c c e" , "C 2/c 2/c 2/e" , "Ccce" , "2ba-c", Bravais::C, 8, 325}, { 68, "D2h^22", "A 2 2 -1ac" , "A e a a" , "A 2/e 2/a 2/a" , "Aeaa" , "1cab" , Bravais::A, 8, 326}, { 68, "D2h^22", "-A 2a 2c" , "A e a a" , "A 2/e 2/a 2/a" , "Aeaa" , "2cab" , Bravais::A, 8, 327}, { 68, "D2h^22", "A 2 2 -1ac" , "A e a a" , "A 2/e 2/a 2/a" , "Aeaa" , "1-cba", Bravais::A, 8, 328}, { 68, "D2h^22", "-A 2ac 2c" , "A e a a" , "A 2/e 2/a 2/a" , "Aeaa" , "2-cba", Bravais::A, 8, 329}, { 68, "D2h^22", "B 2 2 -1bc" , "B b e b" , "B 2/b 2/e 2/b" , "Bbeb" , "1bca" , Bravais::P, 8, 330}, { 68, "D2h^22", "-B 2bc 2b" , "B b c b" , "B 2/b 2/e 2/b" , "Bbcb" , "2bca" , Bravais::P, 8, 331}, { 68, "D2h^22", "B 2 2 -1bc" , "B b e b" , "B 2/b 2/e 2/b" , "Bbeb" , "1a-cb", Bravais::P, 8, 332}, { 68, "D2h^22", "-B 2b 2bc" , "B b e b" , "B 2/b 2/e 2/b" , "Bbeb" , "2a-cb", Bravais::P, 8, 333}, { 69, "D2h^23", "-F 2 2" , "F m m m" , "F 2/m 2/m 2/m" , "Fmmm" , "" , Bravais::F, 8, 334}, { 70, "D2h^24", "F 2 2 -1d" , "F d d d" , "F 2/d 2/d 2/d" , "Fddd" , "1" , Bravais::F, 8, 335}, { 70, "D2h^24", "-F 2uv 2vw" , "F d d d" , "F 2/d 2/d 2/d" , "Fddd" , "2" , Bravais::F, 8, 336}, { 71, "D2h^25", "-I 2 2" , "I m m m" , "I 2/m 2/m 2/m" , "Immm" , "" , Bravais::I, 8, 337}, { 72, "D2h^26", "-I 2 2c" , "I b a m" , "I 2/b 2/a 2/m" , "Ibam" , "" , Bravais::I, 8, 338}, { 72, "D2h^26", "-I 2a 2" , "I m c b" , "I 2/m 2/c 2/b" , "Imcb" , "cab" , Bravais::I, 8, 339}, { 72, "D2h^26", "-I 2b 2b" , "I c m a" , "I 2/c 2/m 2/a" , "Icma" , "bca" , Bravais::I, 8, 340}, { 73, "D2h^27", "-I 2b 2c" , "I b c a" , "I 2/b 2/c 2/a" , "Ibca" , "" , Bravais::I, 8, 341}, { 73, "D2h^27", "-I 2a 2b" , "I c a b" , "I 2/c 2/a 2/b" , "Icab" , "ba-c" , Bravais::I, 8, 342}, { 74, "D2h^28", "-I 2b 2" , "I m m a" , "I 2/m 2/m 2/a" , "Imma" , "" , Bravais::I, 8, 343}, { 74, "D2h^28", "-I 2a 2a" , "I m m b" , "I 2/m 2/m 2/b" , "Immb" , "ba-c" , Bravais::I, 8, 344}, { 74, "D2h^28", "-I 2c 2c" , "I b m m" , "I 2/b 2/m 2/m" , "Ibmm" , "cab" , Bravais::I, 8, 345}, { 74, "D2h^28", "-I 2 2b" , "I c m m" , "I 2/c 2/m 2/m" , "Icmm" , "-cba" , Bravais::I, 8, 346}, { 74, "D2h^28", "-I 2 2a" , "I m c m" , "I 2/m 2/c 2/m" , "Imcm" , "bca" , Bravais::I, 8, 347}, { 74, "D2h^28", "-I 2c 2" , "I m a m" , "I 2/m 2/a 2/m" , "Imam" , "a-cb" , Bravais::I, 8, 348}, { 75, "C4^1" , "P 4" , "P 4" , "P 4" , "P4" , "" , Bravais::P, 9, 349}, { 76, "C4^2" , "P 4w" , "P 4_1" , "P 4_1" , "P4_1" , "" , Bravais::P, 9, 350}, { 77, "C4^3" , "P 4c" , "P 4_2" , "P 4_2" , "P4_2" , "" , Bravais::P, 9, 351}, { 78, "C4^4" , "P 4cw" , "P 4_3" , "P 4_3" , "P4_3" , "" , Bravais::P, 9, 352}, { 79, "C4^5" , "I 4" , "I 4" , "I 4" , "I4" , "" , Bravais::I, 9, 353}, { 80, "C4^6" , "I 4bw" , "I 4_1" , "I 4_1" , "I4_1" , "" , Bravais::I, 9, 354}, { 81, "S4^1" , "P -4" , "P -4" , "P -4" , "P-4" , "" , Bravais::P, 10, 355}, { 82, "S4^2" , "I -4" , "I -4" , "I -4" , "I-4" , "" , Bravais::I, 10, 356}, { 83, "C4h^1" , "-P 4" , "P 4/m" , "P 4/m" , "P4/m" , "" , Bravais::P, 11, 357}, { 84, "C4h^2" , "-P 4c" , "P 4_2/m" , "P 4_2/m" , "P4_2/m" , "" , Bravais::P, 11, 358}, { 85, "C4h^3" , "P 4ab -1ab" , "P 4/n" , "P 4/n" , "P4/n" , "1" , Bravais::P, 11, 359}, { 85, "C4h^3" , "-P 4a" , "P 4/n" , "P 4/n" , "P4/n" , "2" , Bravais::P, 11, 360}, { 86, "C4h^4" , "P 4n -1n" , "P 4_2/n" , "P 4_2/n" , "P4_2/n" , "1" , Bravais::P, 11, 361}, { 86, "C4h^4" , "-P 4bc" , "P 4_2/n" , "P 4_2/n" , "P4_2/n" , "2" , Bravais::P, 11, 362}, { 87, "C4h^5" , "-I 4" , "I 4/m" , "I 4/m" , "I4/m" , "" , Bravais::I, 11, 363}, { 88, "C4h^6" , "I 4bw -1bw" , "I 4_1/a" , "I 4_1/a" , "I4_1/a" , "1" , Bravais::I, 11, 364}, { 88, "C4h^6" , "-I 4ad" , "I 4_1/a" , "I 4_1/a" , "I4_1/a" , "2" , Bravais::I, 11, 365}, { 89, "D4^1" , "P 4 2" , "P 4 2 2" , "P 4 2 2" , "P422" , "" , Bravais::P, 12, 366}, { 90, "D4^2" , "P 4ab 2ab" , "P 4 2_1 2" , "P 4 2_1 2" , "P42_12" , "" , Bravais::P, 12, 367}, { 91, "D4^3" , "P 4w 2c" , "P 4_1 2 2" , "P 4_1 2 2" , "P4_122" , "" , Bravais::P, 12, 368}, { 92, "D4^4" , "P 4abw 2nw" , "P 4_1 2_1 2" , "P 4_1 2_1 2" , "P4_12_12" , "" , Bravais::P, 12, 369}, { 93, "D4^5" , "P 4c 2" , "P 4_2 2 2" , "P 4_2 2 2" , "P4_222" , "" , Bravais::P, 12, 370}, { 94, "D4^6" , "P 4n 2n" , "P 4_2 2_1 2" , "P 4_2 2_1 2" , "P4_22_12" , "" , Bravais::P, 12, 371}, { 95, "D4^7" , "P 4cw 2c" , "P 4_3 2 2" , "P 4_3 2 2" , "P4_322" , "" , Bravais::P, 12, 372}, { 96, "D4^8" , "P 4nw 2abw" , "P 4_3 2_1 2" , "P 4_3 2_1 2" , "P4_32_12" , "" , Bravais::P, 12, 373}, { 97, "D4^9" , "I 4 2" , "I 4 2 2" , "I 4 2 2" , "I422" , "" , Bravais::I, 12, 374}, { 98, "D4^10" , "I 4bw 2bw" , "I 4_1 2 2" , "I 4_1 2 2" , "I4_122" , "" , Bravais::I, 12, 375}, { 99, "C4v^1" , "P 4 -2" , "P 4 m m" , "P 4 m m" , "P4mm" , "" , Bravais::P, 13, 376}, {100, "C4v^2" , "P 4 -2ab" , "P 4 b m" , "P 4 b m" , "P4bm" , "" , Bravais::P, 13, 377}, {101, "C4v^3" , "P 4c -2c" , "P 4_2 c m" , "P 4_2 c m" , "P4_2cm" , "" , Bravais::P, 13, 378}, {102, "C4v^4" , "P 4n -2n" , "P 4_2 n m" , "P 4_2 n m" , "P4_2nm" , "" , Bravais::P, 13, 379}, {103, "C4v^5" , "P 4 -2c" , "P 4 c c" , "P 4 c c" , "P4cc" , "" , Bravais::P, 13, 380}, {104, "C4v^6" , "P 4 -2n" , "P 4 n c" , "P 4 n c" , "P4nc" , "" , Bravais::P, 13, 381}, {105, "C4v^7" , "P 4c -2" , "P 4_2 m c" , "P 4_2 m c" , "P4_2mc" , "" , Bravais::P, 13, 382}, {106, "C4v^8" , "P 4c -2ab" , "P 4_2 b c" , "P 4_2 b c" , "P4_2bc" , "" , Bravais::P, 13, 383}, {107, "C4v^9" , "I 4 -2" , "I 4 m m" , "I 4 m m" , "I4mm" , "" , Bravais::I, 13, 384}, {108, "C4v^10", "I 4 -2c" , "I 4 c m" , "I 4 c m" , "I4cm" , "" , Bravais::I, 13, 385}, {109, "C4v^11", "I 4bw -2" , "I 4_1 m d" , "I 4_1 m d" , "I4_1md" , "" , Bravais::I, 13, 386}, {110, "C4v^12", "I 4bw -2c" , "I 4_1 c d" , "I 4_1 c d" , "I4_1cd" , "" , Bravais::I, 13, 387}, {111, "D2d^1" , "P -4 2" , "P -4 2 m" , "P -4 2 m" , "P-42m" , "" , Bravais::P, 14, 388}, {112, "D2d^2" , "P -4 2c" , "P -4 2 c" , "P -4 2 c" , "P-42c" , "" , Bravais::P, 14, 389}, {113, "D2d^3" , "P -4 2ab" , "P -4 2_1 m" , "P -4 2_1 m" , "P-42_1m" , "" , Bravais::P, 14, 390}, {114, "D2d^4" , "P -4 2n" , "P -4 2_1 c" , "P -4 2_1 c" , "P-42_1c" , "" , Bravais::P, 14, 391}, {115, "D2d^5" , "P -4 -2" , "P -4 m 2" , "P -4 m 2" , "P-4m2" , "" , Bravais::P, 14, 392}, {116, "D2d^6" , "P -4 -2c" , "P -4 c 2" , "P -4 c 2" , "P-4c2" , "" , Bravais::P, 14, 393}, {117, "D2d^7" , "P -4 -2ab" , "P -4 b 2" , "P -4 b 2" , "P-4b2" , "" , Bravais::P, 14, 394}, {118, "D2d^8" , "P -4 -2n" , "P -4 n 2" , "P -4 n 2" , "P-4n2" , "" , Bravais::P, 14, 395}, {119, "D2d^9" , "I -4 -2" , "I -4 m 2" , "I -4 m 2" , "I-4m2" , "" , Bravais::I, 14, 396}, {120, "D2d^10", "I -4 -2c" , "I -4 c 2" , "I -4 c 2" , "I-4c2" , "" , Bravais::I, 14, 397}, {121, "D2d^11", "I -4 2" , "I -4 2 m" , "I -4 2 m" , "I-42m" , "" , Bravais::I, 14, 398}, {122, "D2d^12", "I -4 2bw" , "I -4 2 d" , "I -4 2 d" , "I-42d" , "" , Bravais::I, 14, 399}, {123, "D4h^1" , "-P 4 2" , "P 4/m m m" , "P 4/m 2/m 2/m" , "P4/mmm" , "" , Bravais::P, 15, 400}, {124, "D4h^2" , "-P 4 2c" , "P 4/m c c" , "P 4/m 2/c 2/c" , "P4/mcc" , "" , Bravais::P, 15, 401}, {125, "D4h^3" , "P 4 2 -1ab" , "P 4/n b m" , "P 4/n 2/b 2/m" , "P4/nbm" , "1" , Bravais::P, 15, 402}, {125, "D4h^3" , "-P 4a 2b" , "P 4/n b m" , "P 4/n 2/b 2/m" , "P4/nbm" , "2" , Bravais::P, 15, 403}, {126, "D4h^4" , "P 4 2 -1n" , "P 4/n n c" , "P 4/n 2/n 2/c" , "P4/nnc" , "1" , Bravais::P, 15, 404}, {126, "D4h^4" , "-P 4a 2bc" , "P 4/n n c" , "P 4/n 2/n 2/c" , "P4/nnc" , "2" , Bravais::P, 15, 405}, {127, "D4h^5" , "-P 4 2ab" , "P 4/m b m" , "P 4/m 2_1/b m" , "P4/mbm" , "" , Bravais::P, 15, 406}, {128, "D4h^6" , "-P 4 2n" , "P 4/m n c" , "P 4/m 2_1/n c" , "P4/mnc" , "" , Bravais::P, 15, 407}, {129, "D4h^7" , "P 4ab 2ab -1ab" , "P 4/n m m" , "P 4/n 2_1/m m" , "P4/nmm" , "1" , Bravais::P, 15, 408}, {129, "D4h^7" , "-P 4a 2a" , "P 4/n m m" , "P 4/n 2_1/m m" , "P4/nmm" , "2" , Bravais::P, 15, 409}, {130, "D4h^8" , "P 4ab 2n -1ab" , "P 4/n c c" , "P 4/n 2_1/c c" , "P4/ncc" , "1" , Bravais::P, 15, 410}, {130, "D4h^8" , "-P 4a 2ac" , "P 4/n c c" , "P 4/n 2_1/c c" , "P4/ncc" , "2" , Bravais::P, 15, 411}, {131, "D4h^9" , "-P 4c 2" , "P 4_2/m m c" , "P 4_2/m 2/m 2/c" , "P4_2/mmc" , "" , Bravais::P, 15, 412}, {132, "D4h^10", "-P 4c 2c" , "P 4_2/m c m" , "P 4_2/m 2/c 2/m" , "P4_2/mcm" , "" , Bravais::P, 15, 413}, {133, "D4h^11", "P 4n 2c -1n" , "P 4_2/n b c" , "P 4_2/n 2/b 2/c" , "P4_2/nbc" , "1" , Bravais::P, 15, 414}, {133, "D4h^11", "-P 4ac 2b" , "P 4_2/n b c" , "P 4_2/n 2/b 2/c" , "P4_2/nbc" , "2" , Bravais::P, 15, 415}, {134, "D4h^12", "P 4n 2 -1n" , "P 4_2/n n m" , "P 4_2/n 2/n 2/m" , "P4_2/nnm" , "1" , Bravais::P, 15, 416}, {134, "D4h^12", "-P 4ac 2bc" , "P 4_2/n n m" , "P 4_2/n 2/n 2/m" , "P4_2/nnm" , "2" , Bravais::P, 15, 417}, {135, "D4h^13", "-P 4c 2ab" , "P 4_2/m b c" , "P 4_2/m 2_1/b 2/c" , "P4_2/mbc" , "" , Bravais::P, 15, 418}, {136, "D4h^14", "-P 4n 2n" , "P 4_2/m n m" , "P 4_2/m 2_1/n 2/m" , "P4_2/mnm" , "" , Bravais::P, 15, 419}, {137, "D4h^15", "P 4n 2n -1n" , "P 4_2/n m c" , "P 4_2/n 2_1/m 2/c" , "P4_2/nmc" , "1" , Bravais::P, 15, 420}, {137, "D4h^15", "-P 4ac 2a" , "P 4_2/n m c" , "P 4_2/n 2_1/m 2/c" , "P4_2/nmc" , "2" , Bravais::P, 15, 421}, {138, "D4h^16", "P 4n 2ab -1n" , "P 4_2/n c m" , "P 4_2/n 2_1/c 2/m" , "P4_2/ncm" , "1" , Bravais::P, 15, 422}, {138, "D4h^16", "-P 4ac 2ac" , "P 4_2/n c m" , "P 4_2/n 2_1/c 2/m" , "P4_2/ncm" , "2" , Bravais::P, 15, 423}, {139, "D4h^17", "-I 4 2" , "I 4/m m m" , "I 4/m 2/m 2/m" , "I4/mmm" , "" , Bravais::I, 15, 424}, {140, "D4h^18", "-I 4 2c" , "I 4/m c m" , "I 4/m 2/c 2/m" , "I4/mcm" , "" , Bravais::I, 15, 425}, {141, "D4h^19", "I 4bw 2bw -1bw" , "I 4_1/a m d" , "I 4_1/a 2/m 2/d" , "I4_1/amd" , "1" , Bravais::I, 15, 426}, {141, "D4h^19", "-I 4bd 2" , "I 4_1/a m d" , "I 4_1/a 2/m 2/d" , "I4_1/amd" , "2" , Bravais::I, 15, 427}, {142, "D4h^20", "I 4bw 2aw -1bw" , "I 4_1/a c d" , "I 4_1/a 2/c 2/d" , "I4_1/acd" , "1" , Bravais::I, 15, 428}, {142, "D4h^20", "-I 4bd 2c" , "I 4_1/a c d" , "I 4_1/a 2/c 2/d" , "I4_1/acd" , "2" , Bravais::I, 15, 429}, {143, "C3^1" , "P 3" , "P 3" , "P 3" , "P3" , "" , Bravais::P, 16, 430}, {144, "C3^2" , "P 31" , "P 3_1" , "P 3_1" , "P3_1" , "" , Bravais::P, 16, 431}, {145, "C3^3" , "P 32" , "P 3_2" , "P 3_2" , "P3_2" , "" , Bravais::P, 16, 432}, {146, "C3^4" , "R 3" , "R 3" , "R 3" , "R3" , "H" , Bravais::R, 16, 433}, {146, "C3^4" , "P 3*" , "R 3" , "R 3" , "R3" , "R" , Bravais::P, 16, 434}, {147, "C3i^1" , "-P 3" , "P -3" , "P -3" , "P-3" , "" , Bravais::P, 17, 435}, {148, "C3i^2" , "-R 3" , "R -3" , "R -3" , "R-3" , "H" , Bravais::R, 17, 436}, {148, "C3i^2" , "-P 3*" , "R -3" , "R -3" , "R-3" , "R" , Bravais::P, 17, 437}, {149, "D3^1" , "P 3 2" , "P 3 1 2" , "P 3 1 2" , "P312" , "" , Bravais::P, 18, 438}, {150, "D3^2" , "P 3 2\"" , "P 3 2 1" , "P 3 2 1" , "P321" , "" , Bravais::P, 18, 439}, {151, "D3^3" , "P 31 2c (0 0 1)" , "P 3_1 1 2" , "P 3_1 1 2" , "P3_112" , "" , Bravais::P, 18, 440}, {152, "D3^4" , "P 31 2\"" , "P 3_1 2 1" , "P 3_1 2 1" , "P3_121" , "" , Bravais::P, 18, 441}, {153, "D3^5" , "P 32 2c (0 0 -1)", "P 3_2 1 2" , "P 3_2 1 2" , "P3_212" , "" , Bravais::P, 18, 442}, {154, "D3^6" , "P 32 2\"" , "P 3_2 2 1" , "P 3_2 2 1" , "P3_221" , "" , Bravais::P, 18, 443}, {155, "D3^7" , "R 3 2\"" , "R 3 2" , "R 3 2" , "R32" , "H" , Bravais::R, 18, 444}, {155, "D3^7" , "P 3* 2" , "R 3 2" , "R 3 2" , "R32" , "R" , Bravais::P, 18, 445}, {156, "C3v^1" , "P 3 -2\"" , "P 3 m 1" , "P 3 m 1" , "P3m1" , "" , Bravais::P, 19, 446}, {157, "C3v^2" , "P 3 -2" , "P 3 1 m" , "P 3 1 m" , "P31m" , "" , Bravais::P, 19, 447}, {158, "C3v^3" , "P 3 -2\"c" , "P 3 c 1" , "P 3 c 1" , "P3c1" , "" , Bravais::P, 19, 448}, {159, "C3v^4" , "P 3 -2c" , "P 3 1 c" , "P 3 1 c" , "P31c" , "" , Bravais::P, 19, 449}, {160, "C3v^5" , "R 3 -2\"" , "R 3 m" , "R 3 m" , "R3m" , "H" , Bravais::R, 19, 450}, {160, "C3v^5" , "P 3* -2" , "R 3 m" , "R 3 m" , "R3m" , "R" , Bravais::P, 19, 451}, {161, "C3v^6" , "R 3 -2\"c" , "R 3 c" , "R 3 c" , "R3c" , "H" , Bravais::R, 19, 452}, {161, "C3v^6" , "P 3* -2n" , "R 3 c" , "R 3 c" , "R3c" , "R" , Bravais::P, 19, 453}, {162, "D3d^1" , "-P 3 2" , "P -3 1 m" , "P -3 1 2/m" , "P-31m" , "" , Bravais::P, 20, 454}, {163, "D3d^2" , "-P 3 2c" , "P -3 1 c" , "P -3 1 2/c" , "P-31c" , "" , Bravais::P, 20, 455}, {164, "D3d^3" , "-P 3 2\"" , "P -3 m 1" , "P -3 2/m 1" , "P-3m1" , "" , Bravais::P, 20, 456}, {165, "D3d^4" , "-P 3 2\"c" , "P -3 c 1" , "P -3 2/c 1" , "P-3c1" , "" , Bravais::P, 20, 457}, {166, "D3d^5" , "-R 3 2\"" , "R -3 m" , "R -3 2/m" , "R-3m" , "H" , Bravais::R, 20, 458}, {166, "D3d^5" , "-P 3* 2" , "R -3 m" , "R -3 2/m" , "R-3m" , "R" , Bravais::P, 20, 459}, {167, "D3d^6" , "-R 3 2\"c" , "R -3 c" , "R -3 2/c" , "R-3c" , "H" , Bravais::R, 20, 460}, {167, "D3d^6" , "-P 3* 2n" , "R -3 c" , "R -3 2/c" , "R-3c" , "R" , Bravais::P, 20, 461}, {168, "C6^1" , "P 6" , "P 6" , "P 6" , "P6" , "" , Bravais::P, 21, 462}, {169, "C6^2" , "P 61" , "P 6_1" , "P 6_1" , "P6_1" , "" , Bravais::P, 21, 463}, {170, "C6^3" , "P 65" , "P 6_5" , "P 6_5" , "P6_5" , "" , Bravais::P, 21, 464}, {171, "C6^4" , "P 62" , "P 6_2" , "P 6_2" , "P6_2" , "" , Bravais::P, 21, 465}, {172, "C6^5" , "P 64" , "P 6_4" , "P 6_4" , "P6_4" , "" , Bravais::P, 21, 466}, {173, "C6^6" , "P 6c" , "P 6_3" , "P 6_3" , "P6_3" , "" , Bravais::P, 21, 467}, {174, "C3h^1" , "P -6" , "P -6" , "P -6" , "P-6" , "" , Bravais::P, 22, 468}, {175, "C6h^1" , "-P 6" , "P 6/m" , "P 6/m" , "P6/m" , "" , Bravais::P, 23, 469}, {176, "C6h^2" , "-P 6c" , "P 6_3/m" , "P 6_3/m" , "P6_3/m" , "" , Bravais::P, 23, 470}, {177, "D6^1" , "P 6 2" , "P 6 2 2" , "P 6 2 2" , "P622" , "" , Bravais::P, 24, 471}, {178, "D6^2" , "P 61 2 (0 0 -1)" , "P 6_1 2 2" , "P 6_1 2 2" , "P6_122" , "" , Bravais::P, 24, 472}, {179, "D6^3" , "P 65 2 (0 0 1)" , "P 6_5 2 2" , "P 6_5 2 2" , "P6_522" , "" , Bravais::P, 24, 473}, {180, "D6^4" , "P 62 2c (0 0 1)" , "P 6_2 2 2" , "P 6_2 2 2" , "P6_222" , "" , Bravais::P, 24, 474}, {181, "D6^5" , "P 64 2c (0 0 -1)", "P 6_4 2 2" , "P 6_4 2 2" , "P6_422" , "" , Bravais::P, 24, 475}, {182, "D6^6" , "P 6c 2c" , "P 6_3 2 2" , "P 6_3 2 2" , "P6_322" , "" , Bravais::P, 24, 476}, {183, "C6v^1" , "P 6 -2" , "P 6 m m" , "P 6 m m" , "P6mm" , "" , Bravais::P, 25, 477}, {184, "C6v^2" , "P 6 -2c" , "P 6 c c" , "P 6 c c" , "P6cc" , "" , Bravais::P, 25, 478}, {185, "C6v^3" , "P 6c -2" , "P 6_3 c m" , "P 6_3 c m" , "P6_3cm" , "" , Bravais::P, 25, 479}, {186, "C6v^4" , "P 6c -2c" , "P 6_3 m c" , "P 6_3 m c" , "P6_3mc" , "" , Bravais::P, 25, 480}, {187, "D3h^1" , "P -6 2" , "P -6 m 2" , "P -6 m 2" , "P-6m2" , "" , Bravais::P, 26, 481}, {188, "D3h^2" , "P -6c 2" , "P -6 c 2" , "P -6 c 2" , "P-6c2" , "" , Bravais::P, 26, 482}, {189, "D3h^3" , "P -6 -2" , "P -6 2 m" , "P -6 2 m" , "P-62m" , "" , Bravais::P, 26, 483}, {190, "D3h^4" , "P -6c -2c" , "P -6 2 c" , "P -6 2 c" , "P-62c" , "" , Bravais::P, 26, 484}, {191, "D6h^1" , "-P 6 2" , "P 6/m m m" , "P 6/m 2/m 2/m" , "P6/mmm" , "" , Bravais::P, 27, 485}, {192, "D6h^2" , "-P 6 2c" , "P 6/m c c" , "P 6/m 2/c 2/c" , "P6/mcc" , "" , Bravais::P, 27, 486}, {193, "D6h^3" , "-P 6c 2" , "P 6_3/m c m" , "P 6_3/m 2/c 2/m" , "P6_3/mcm" , "" , Bravais::P, 27, 487}, {194, "D6h^4" , "-P 6c 2c" , "P 6_3/m m c" , "P 6_3/m 2/m 2/c" , "P6_3/mmc" , "" , Bravais::P, 27, 488}, {195, "T^1" , "P 2 2 3" , "P 2 3" , "P 2 3" , "P23" , "" , Bravais::P, 28, 489}, {196, "T^2" , "F 2 2 3" , "F 2 3" , "F 2 3" , "F23" , "" , Bravais::F, 28, 490}, {197, "T^3" , "I 2 2 3" , "I 2 3" , "I 2 3" , "I23" , "" , Bravais::I, 28, 491}, {198, "T^4" , "P 2ac 2ab 3" , "P 2_1 3" , "P 2_1 3" , "P2_13" , "" , Bravais::P, 28, 492}, {199, "T^5" , "I 2b 2c 3" , "I 2_1 3" , "I 2_1 3" , "I2_13" , "" , Bravais::I, 28, 493}, {200, "Th^1" , "-P 2 2 3" , "P m -3" , "P 2/m -3" , "Pm-3" , "" , Bravais::P, 29, 494}, {201, "Th^2" , "P 2 2 3 -1n" , "P n -3" , "P 2/n -3" , "Pn-3" , "1" , Bravais::P, 29, 495}, {201, "Th^2" , "-P 2ab 2bc 3" , "P n -3" , "P 2/n -3" , "Pn-3" , "2" , Bravais::P, 29, 496}, {202, "Th^3" , "-F 2 2 3" , "F m -3" , "F 2/m -3" , "Fm-3" , "" , Bravais::F, 29, 497}, {203, "Th^4" , "F 2 2 3 -1d" , "F d -3" , "F 2/d -3" , "Fd-3" , "1" , Bravais::F, 29, 498}, {203, "Th^4" , "-F 2uv 2vw 3" , "F d -3" , "F 2/d -3" , "Fd-3" , "2" , Bravais::F, 29, 499}, {204, "Th^5" , "-I 2 2 3" , "I m -3" , "I 2/m -3" , "Im-3" , "" , Bravais::I, 29, 500}, {205, "Th^6" , "-P 2ac 2ab 3" , "P a -3" , "P 2_1/a -3" , "Pa-3" , "" , Bravais::P, 29, 501}, {206, "Th^7" , "-I 2b 2c 3" , "I a -3" , "I 2_1/a -3" , "Ia-3" , "" , Bravais::I, 29, 502}, {207, "O^1" , "P 4 2 3" , "P 4 3 2" , "P 4 3 2" , "P432" , "" , Bravais::P, 30, 503}, {208, "O^2" , "P 4n 2 3" , "P 4_2 3 2" , "P 4_2 3 2" , "P4_232" , "" , Bravais::P, 30, 504}, {209, "O^3" , "F 4 2 3" , "F 4 3 2" , "F 4 3 2" , "F432" , "" , Bravais::F, 30, 505}, {210, "O^4" , "F 4d 2 3" , "F 4_1 3 2" , "F 4_1 3 2" , "F4_132" , "" , Bravais::F, 30, 506}, {211, "O^5" , "I 4 2 3" , "I 4 3 2" , "I 4 3 2" , "I432" , "" , Bravais::I, 30, 507}, {212, "O^6" , "P 4acd 2ab 3" , "P 4_3 3 2" , "P 4_3 3 2" , "P4_332" , "" , Bravais::P, 30, 508}, {213, "O^7" , "P 4bd 2ab 3" , "P 4_1 3 2" , "P 4_1 3 2" , "P4_132" , "" , Bravais::P, 30, 509}, {214, "O^8" , "I 4bd 2c 3" , "I 4_1 3 2" , "I 4_1 3 2" , "I4_132" , "" , Bravais::I, 30, 510}, {215, "Td^1" , "P -4 2 3" , "P -4 3 m" , "P -4 3 m" , "P-43m" , "" , Bravais::P, 31, 511}, {216, "Td^2" , "F -4 2 3" , "F -4 3 m" , "F -4 3 m" , "F-43m" , "" , Bravais::F, 31, 512}, {217, "Td^3" , "I -4 2 3" , "I -4 3 m" , "I -4 3 m" , "I-43m" , "" , Bravais::I, 31, 513}, {218, "Td^4" , "P -4n 2 3" , "P -4 3 n" , "P -4 3 n" , "P-43n" , "" , Bravais::P, 31, 514}, {219, "Td^5" , "F -4c 2 3" , "F -4 3 c" , "F -4 3 c" , "F-43c" , "" , Bravais::F, 31, 515}, {220, "Td^6" , "I -4bd 2c 3" , "I -4 3 d" , "I -4 3 d" , "I-43d" , "" , Bravais::I, 31, 516}, {221, "Oh^1" , "-P 4 2 3" , "P m -3 m" , "P 4/m -3 2/m" , "Pm-3m" , "" , Bravais::P, 32, 517}, {222, "Oh^2" , "P 4 2 3 -1n" , "P n -3 n" , "P 4/n -3 2/n" , "Pn-3n" , "1" , Bravais::P, 32, 518}, {222, "Oh^2" , "-P 4a 2bc 3" , "P n -3 n" , "P 4/n -3 2/n" , "Pn-3n" , "2" , Bravais::P, 32, 519}, {223, "Oh^3" , "-P 4n 2 3" , "P m -3 n" , "P 4_2/m -3 2/n" , "Pm-3n" , "" , Bravais::P, 32, 520}, {224, "Oh^4" , "P 4n 2 3 -1n" , "P n -3 m" , "P 4_2/n -3 2/m" , "Pn-3m" , "1" , Bravais::P, 32, 521}, {224, "Oh^4" , "-P 4bc 2bc 3" , "P n -3 m" , "P 4_2/n -3 2/m" , "Pn-3m" , "2" , Bravais::P, 32, 522}, {225, "Oh^5" , "-F 4 2 3" , "F m -3 m" , "F 4/m -3 2/m" , "Fm-3m" , "" , Bravais::F, 32, 523}, {226, "Oh^6" , "-F 4c 2 3" , "F m -3 c" , "F 4/m -3 2/c" , "Fm-3c" , "" , Bravais::F, 32, 524}, {227, "Oh^7" , "F 4d 2 3 -1d" , "F d -3 m" , "F 4_1/d -3 2/m" , "Fd-3m" , "1" , Bravais::F, 32, 525}, {227, "Oh^7" , "-F 4vw 2vw 3" , "F d -3 m" , "F 4_1/d -3 2/m" , "Fd-3m" , "2" , Bravais::F, 32, 526}, {228, "Oh^8" , "F 4d 2 3 -1cd" , "F d -3 c" , "F 4_1/d -3 2/c" , "Fd-3c" , "1" , Bravais::F, 32, 527}, {228, "Oh^8" , "-F 4cvw 2vw 3" , "F d -3 c" , "F 4_1/d -3 2/c" , "Fd-3c" , "2" , Bravais::F, 32, 528}, {229, "Oh^9" , "-I 4 2 3" , "I m -3 m" , "I 4/m -3 2/m" , "Im-3m" , "" , Bravais::I, 32, 529}, {230, "Oh^10" , "-I 4bd 2c 3" , "I a -3 d" , "I 4_1/a -3 2/d" , "Ia-3d" , "" , Bravais::I, 32, 530}, }; bool brille::hall_number_ok(const int h) {return h>0 && h<531;} int brille::international_number_to_hall_number(const int n, const std::string& c){ if (n>=0 && n<230) for (int i=1; i<531; i++){ Spacegroup spg(ALL_SPACEGROUPS[i]); if (n==spg.number && (0==c.size() || 0==c.compare(spg.choice))) return i; } return -1; } int brille::international_string_to_hall_number(const std::string& n, const std::string& c){ for (int i=1; i<531; i++) { Spacegroup spg(ALL_SPACEGROUPS[i]); // now check for matching international table names if( (0==c.size() || 0==c.compare(spg.choice)) && ( 0==n.compare(spg.international) || 0==n.compare(spg.international_full) || 0==n.compare(spg.international_short)) ) return i; } return 0; // no matching strings } int brille::hall_symbol_to_hall_number(const std::string& hsymbol){ for (int i=1; i<531; i++){ Spacegroup spg(ALL_SPACEGROUPS[i]); // only accept exact matches if (0==hsymbol.compare(spg.hall_symbol)) return i; } return 0; // no exact matches } // When we don't know if we're searching for a Hall Symbol or // International Table Name/Symbol search for either, starting with Hall symbols int brille::string_to_hall_number(const std::string& str, const std::string& ch){ int tmp = brille::hall_symbol_to_hall_number(str); if (!tmp) tmp = brille::international_string_to_hall_number(str, ch); return tmp; } void Spacegroup::set_from_hall_number(const int hn){ Spacegroup spg(ALL_SPACEGROUPS[brille::hall_number_ok(hn) ? hn : 0]); this->number = spg.number; this->schoenflies = spg.schoenflies; this->hall_symbol = spg.hall_symbol; this->international = spg.international; this->international_full = spg.international_full; this->international_short = spg.international_short; this->choice = spg.choice; this->bravais = spg.bravais; this->pointgroup_number = spg.pointgroup_number; this->hall_number = spg.hall_number; } Symmetry Spacegroup::get_spacegroup_symmetry() const { HallSymbol hs(this->hall_symbol); Symmetry generators = hs.get_generators(); Symmetry fullsym = generators.generate(); return fullsym; } PointSymmetry Spacegroup::get_pointgroup_symmetry(const int time_reversal) const{ Symmetry sym = this->get_spacegroup_symmetry(); std::vector> uniqrots = get_unique_rotations(sym.getallr(), time_reversal); return PointSymmetry(uniqrots); }