International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 3.5, pp. 839-841

Table 3.5.2.4 

E. Koch,a W. Fischera and U. Müllerb

Table 3.5.2.4| top | pdf |
Euclidean and chirality-preserving Euclidean normalizers of the orthorhombic space groups

The symbols in parentheses following a space-group symbol refer to the location of the origin (`origin choice' in Chapter 2.3[link] ).

Space group [{\cal G}]Euclidean normalizer [\cal N_E(G)] and chirality-preserving normalizer [\cal N_{E^+}(G)]Additional generators of [\cal N_E(G)] and [\cal N_{E^+}(G)]Index of [{\cal G}] in [{\cal N_E(G)}] or [\cal N_{E^+}(G)]
No.Hermann–Mauguin symbolCell metricSymbolBasis vectorsTranslationsInversion through a centre atFurther generators
16 [P222] [a\neq b\neq c\neq a] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0]   [8\cdot 2\cdot 1]
      [{\cal N_{E^+}(G)}\!\!:\; P222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/]   [8\cdot 1]
    [a= b\neq c] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0] [y,x,z] [8\cdot 2\cdot 2]
      [{\cal N_{E^+}(G)}\!\!:\; P422] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/] [y,x,\bar z] [8\cdot 2]
    [a= b=c] [Pm\bar 3m] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0] [z,x,y;\ y,x,z] [8\cdot 2\cdot 6]
      [{\cal N_{E^+}(G)}\!\!:\; P432] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/] [z,x,y;\ y,x,\bar z] [8\cdot 6]
17 [P222_1] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0]   [8\cdot 2\cdot 1]
      [{\cal N_{E^+}(G)}\!\!:\; P222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/]   [8\cdot 1]
    [a= b] [P4_2/mmc] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0] [y,x,z+{\textstyle{1\over 4}}] [8\cdot 2\cdot 2]
      [{\cal N_{E^+}(G)}\!\!:\; P4_222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/] [y,x,\bar z+{\textstyle{1\over 4}}] [8\cdot 2]
18 [P2_12_12] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0]   [8\cdot 2\cdot 1]
      [{\cal N_{E^+}(G)}\!\!:\; P222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/]   [8\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0] [y,x,z] [8\cdot 2\cdot 2]
      [{\cal N_{E^+}(G)}\!\!:\; P422] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/] [y,x,\bar z] [8\cdot 2]
19 [P2_12_12_1] [a\neq b\neq c\neq a] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0]   [8\cdot 2\cdot 1]
      [{\cal N_{E^+}(G)}\!\!:\; P222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/]   [8\cdot 1]
    [a= b\neq c] [P4_2/mmc] [(2/m\,2/m\,n)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0] [y+{\textstyle{1\over 4}},x+{\textstyle{1\over 4}},z+{\textstyle{1\over 4}}] [8\cdot 2\cdot 2]
      [{\cal N_{E^+}(G)}\!\!:\;P4_222] [(222_1)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/] [\bar y+{\textstyle{1\over 4}},\bar x+{\textstyle{1\over 4}},\bar z+{\textstyle{1\over 4}}] [8\cdot 2]
    [a= b=c] [Pm\bar 3n] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0] [z,x,y;\ y+{\textstyle{1\over 4}},x+{\textstyle{1\over 4}},z+{\textstyle{1\over 4}}] [8\cdot 2\cdot 6]
      [{\cal N_{E^+}(G)}\!\!:\; P4_232] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/] [z,x,y;\ \bar y+{\textstyle{1\over 4}},\bar x+{\textstyle{1\over 4}},\bar z+{\textstyle{1\over 4}}] [8\cdot 6]
20 [C222_1] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0]   [4\cdot 2\cdot 1]
      [{\cal N_{E^+}(G)}\!\!:\; P222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}] [/]   [4\cdot 1]
    [a= b] [P4_2/mmc] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0] [y,x,z+{\textstyle{1\over 4}}] [4\cdot 2\cdot 2]
      [{\cal N_{E^+}(G)}\!\!:\;P4_222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}] [/] [y,x,\bar z+{\textstyle{1\over 4}}] [4\cdot 2]
21 [C222] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0]   [4\cdot 2\cdot 1]
      [{\cal N_{E^+}(G)}\!\!:\; P222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}] [/]   [4\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0] [y,x,z] [4\cdot 2\cdot 2]
      [{\cal N_{E^+}(G)}\!\!:\; P422] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}] [/] [y,x,\bar z] [4\cdot 2]
22 [F222] [a\neq b\neq c\neq a] [Immm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 4}},{\textstyle{1\over 4}},{\textstyle{1\over 4}}] [0,0,0]   [4\cdot 2\cdot 1]
      [{\cal N_{E^+}(G)}\!\!:\;I222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 4}},{\textstyle{1\over 4}},{\textstyle{1\over 4}}] [/]   [4\cdot 1]
    [a= b\neq c] [I4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 4}},{\textstyle{1\over 4}},{\textstyle{1\over 4}}] [0,0,0] [y,x,z] [4\cdot 2\cdot 2]
      [{\cal N_{E^+}(G)}\!\!:\;I422] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 4}},{\textstyle{1\over 4}},{\textstyle{1\over 4}}] [/] [y,x,\bar z] [4\cdot 2]
    [a= b=c] [Im\bar 3m] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 4}},{\textstyle{1\over 4}},{\textstyle{1\over 4}}] [0,0,0] [z,x,y;\ y,x,z] [4\cdot 2\cdot 6]
      [{\cal N_{E^+}(G)}\!\!:\; I432] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 4}},{\textstyle{1\over 4}},{\textstyle{1\over 4}}] [/] [z,x,y;\ y,x,\bar z] [4\cdot 6]
23 [I222] [a\neq b\neq c\neq a] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [0,0,0]   [4\cdot 2\cdot 1]
      [{\cal N_{E^+}(G)}\!\!:\;P222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [/]   [4\cdot 1]
    [a= b\neq c] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [0,0,0] [y,x,z] [4\cdot 2\cdot 2]
      [{\cal N_{E^+}(G)}\!\!:\; P422] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [/] [y,x,\bar z] [4\cdot 2]
    [a= b=c] [Pm\bar 3m] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [0,0,0] [z,x,y;\ y,x,z] [4\cdot 2\cdot 6]
      [{\cal N_{E^+}(G)}\!\!:\; P432] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [/] [z,x,y;\ y,x,\bar z] [4\cdot 6]
24 [I2_12_12_1] [a\neq b\neq c\neq a] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [0,0,0]   [4\cdot 2\cdot 1]
      [{\cal N_{E^+}(G)}\!\!:\; P222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [/]   [4\cdot 1]
    [a= b\neq c] [P4_2/mmc] [(2/m\,2/m\,n)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [0,0,0] [y+{\textstyle{1\over 4}},x+{\textstyle{1\over 4}},z+{\textstyle{1\over 4}}] [4\cdot 2\cdot 2]
      [{\cal N_{E^+}(G)}\!\!:\; P4_222] [(222_1)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [/] [\bar y+{\textstyle{1\over 4}},\bar x+{\textstyle{1\over 4}},\bar z+{\textstyle{1\over 4}}] [4\cdot 2]
    [a= b=c] [Pm\bar 3n] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [0,0,0] [z,x,y;\ y+{\textstyle{1\over 4}},x+{\textstyle{1\over 4}},z+{\textstyle{1\over 4}}] [4\cdot 2\cdot 6]
      [{\cal N_{E^+}(G)}\!\!:\; P4_232] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [/] [z,x,y;\ \bar y+{\textstyle{1\over 4}},\bar x+{\textstyle{1\over 4}},\bar z+{\textstyle{1\over 4}}] [4\cdot 6]
25 [Pmm2] [a\neq b] [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
    [a= b] [P^14/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0] [y,x,z] [(4\cdot\infty )\cdot 2\cdot 2]
26 [Pmc2_1]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
27 [Pcc2] [a\neq b] [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
    [a= b] [P^14/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0] [y,x,z] [(4\cdot\infty )\cdot 2\cdot 2]
28 [Pma2]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
29 [Pca2_1]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
30 [Pnc2]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
31 [Pmn2_1]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
32 [Pba2] [a\neq b] [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
    [a= b] [P^14/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0] [y,x,z] [(4\cdot\infty )\cdot 2\cdot 2]
33 [Pna2_1]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
34 [Pnn2] [a\neq b] [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
    [a= b] [P^14/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0] [y,x,z] [(4\cdot\infty )\cdot 2\cdot 2]
35 [Cmm2] [a\neq b] [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
    [a= b] [P^14/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0] [y,x,z] [(2\cdot\infty )\cdot 2\cdot 2]
36 [Cmc2_1]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
37 [Ccc2] [a\neq b] [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
    [a= b] [P^14/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0] [y,x,z] [(2\cdot\infty )\cdot 2\cdot 2]
38 [Amm2]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
39 [Aem2]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
40 [Ama2]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
41 [Aea2]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
42 [Fmm2] [a\neq b] [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [0,0,t] [0,0,0]   [\infty \cdot 2\cdot 1]
    [a= b] [P^14/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [0,0,t] [0,0,0] [y,x,z] [\infty \cdot 2\cdot 2]
43 [Fdd2] [a\neq b] [P^1ban\ (222)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [0,0,t] [{\textstyle{1\over 8}},{\textstyle{1\over 8}},0]   [\infty \cdot 2\cdot 1]
    [a= b] [P^14/nbm] [(\bar 42m)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [0,0,t] [{\textstyle{1\over 8}},{\textstyle{1\over 8}},0] [y,x,z] [\infty \cdot 2\cdot 2]
44 [Imm2] [a\neq b] [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
    [a= b] [P^14/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0] [y,x,z] [(2\cdot\infty )\cdot 2\cdot 2]
45 [Iba2] [a\neq b] [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
    [a= b] [P^14/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0] [y,x,z] [(2\cdot\infty )\cdot 2\cdot 2]
46 [Ima2]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
47 [Pmmm] [a\neq b\neq c\neq a] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
    [a= b\neq c] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\cdot 1\cdot 2]
    [a= b=c] [Pm\bar 3m] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [z,x,y;\ y,x,z] [8\cdot 1\cdot 6]
48 [Pnnn] (both [a\neq b\neq c\neq a] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
  origins) [a= b\neq c] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\cdot 1\cdot 2]
    [a= b=c] [Pm\bar3m] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [z,x,y;\ y,x,z] [8\cdot 1\cdot 6]
49 [Pccm] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\cdot 1\cdot 2]
50 [Pban] (both [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
  origins) [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\cdot 1\cdot 2]
51 [Pmma]   [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
52 [Pnna]   [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
53 [Pmna]   [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
54 [Pcca]   [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
55 [Pbam] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\cdot 1\cdot 2]
56 [Pccn] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\cdot 1\cdot 2]
57 [Pbcm]   [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
58 [Pnnm] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\cdot 1\cdot 2]
59 [Pmmn] (both [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
  origins) [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\cdot 1\cdot 2]
60 [Pbcn]   [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
61 [Pbca] [a\neq b] or [b\neq c] or [a \neq c] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
    [a= b = c] [Pm\bar 3] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [z,x,y] [8\cdot 1\cdot 3]
62 [Pnma]   [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
63 [Cmcm]   [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]     [4\cdot 1\cdot 1]
64 [Cmce]   [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]     [4\cdot 1\cdot 1]
65 [Cmmm] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]     [4\cdot 1\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [4\cdot 1\cdot 2]
66 [Cccm] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]     [4\cdot 1\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [4\cdot 1\cdot 2]
67 [Cmme] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]     [4\cdot 1\cdot 1]
    [a= b] [P4/mmm] [(mmm)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]   [y+{\textstyle{1\over 4}},x-{\textstyle{1\over 4}},z] [4\cdot 1\cdot 2]
68 [Ccce] [(222)] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]     [4\cdot 1\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [4\cdot 1\cdot 2]
68 [Ccce] [(\bar 1)] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]     [4\cdot 1\cdot 1]
    [a= b] [P4/mmm] [(mmm)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]   [y+{\textstyle{1\over 4}},x-{\textstyle{1\over 4}},z] [4\cdot 1\cdot 2]
69 [Fmmm] [a\neq b\neq c\neq a] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0]     [2\cdot 1\cdot 1]
    [a= b\neq c] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0]   [y,x,z] [2\cdot 1\cdot 2]
    [a= b=c] [Pm\bar 3m] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0]   [z,x,y;\ y,x,z] [2\cdot 1\cdot 6]
70 [Fddd] [(222)] [a\neq b\neq c\neq a] [Pnnn] [(222)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0]     [2\cdot 1\cdot 1]
    [a= b\neq c] [P4_2/nnm] [(\bar 42m)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0]   [\bar y,\bar x,z] [2\cdot 1\cdot 2]
    [a= b=c] [Pn\bar 3m] [(\bar 43m)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0]   [z,x,y;\ y,x,z] [2\cdot 1\cdot 6]
70 [Fddd] [(\bar 1)] [a\neq b\neq c\neq a] [Pnnn] [(\bar 1)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0]     [2\cdot 1\cdot 1]
    [a= b\neq c] [P4_2/nnm] ([2/m] at [0,{\textstyle{1\over 2}},0]) [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0]   [y,x,z] [2\cdot 1\cdot 2]
    [a= b=c] [Pn\bar 3m] [(\bar 3m)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0]   [z,x,y;\ y,x,z] [2\cdot 1\cdot 6]
71 [Immm] [a\neq b\neq c\neq a] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]     [4\cdot 1\cdot 1]
    [a= b\neq c] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]   [y,x,z] [4\cdot 1\cdot 2]
    [a= b=c] [Pm\bar 3m] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]   [z,x,y;\ y,x,z] [4\cdot 1\cdot 6]
72 [Ibam] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]     [4\cdot 1\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]   [y,x,z] [4\cdot 1\cdot 2]
73 [Ibca] [a\neq b\neq c\neq a] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]     [4\cdot 1\cdot 1]
    [a= b\neq c] [P4_2/mmc] [(2/m\,2/m\,n)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]   [y+{\textstyle{1\over 4}},x+{\textstyle{1\over 4}},z+{\textstyle{1\over 4}}] [4\cdot 1\cdot 2]
    [a= b=c] [Pm\bar 3n] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]   [z,x,y;\ y+{\textstyle{1\over 4}},x+{\textstyle{1\over 4}},z+{\textstyle{1\over 4}}] [4\cdot 1\cdot 6]
74 [Imma] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]     [4\cdot 1\cdot 1]
    [a= b] [P4_2/mmc] [(2/m\,2/m\,n)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]   [y+{\textstyle{1\over 4}},x-{\textstyle{1\over 4}},z+{\textstyle{1\over 4}}] [4\cdot 1\cdot 2]