Im-3m No. 229 I4/m-32/m Oh9


Axes Coordinates Wyckoff positions
2a 6b 8c 12d 12e 16f 24g
24h 48i 48j 48k 96l
I Maximal translationengleiche subgroups
[2] I-43m 2a 6b 8c 12d 12e 2 × 8c 24f
  (217) 24g 48h 48h 2 × 24g 2 × 48h
[2] I432 2a 6b 8c 12d 12e 16f 24g
  (211) 24h 2 × 24i 48j 48j 2 × 48j
[2] Im-3 2a 6b 8c 12e 12d 16f 2 × 12e
  (204) 24g 48h 2 × 24g 48h 2 × 48h
[4] R-3m (1/2)(-a + b + c), y + z, x + z, x + y 1a 3e 1b; 3d 6g 6h 2c; 6h 12i
  (166) (1/2)(a - b + c), (rhombohedral 6f; 6h 2 × 6g; 12i 2 × 12i 2 × 6h; 12i 4 × 12i
(1/2)(a + b - c) axes)
-a + b, -b + c, (1/3)(-2x + y + z), (1/3)(-x - y + 2z), 3a 9e 3b; 9d 18g 18h 6c; 18h 36i
(1/2)(a + b + c) (2/3)(x + y + z) 18f; 18h 2 × 18g; 36i 2 × 36i 2 × 18h; 36i 4 × 36i
(hexagonal axes)
 conjugate: a + b, -b - c, (1/3)(2x + y - z), (1/3)(x - y - 2z),
(1/2)(-a + b - c) (2/3)(-x + y - z)
(hexagonal axes)
 conjugate: -a - b, b - c, (1/3)(-2x - y - z), (1/3)(-x + y - 2z),
(1/2)(a - b - c) (2/3)(x - y - z)
(hexagonal axes)
 conjugate: a - b, b + c, (1/3)(2x - y + z), (1/3)(x + y + 2z),
(1/2)(-a - b + c) (2/3)(-x - y + z)
(hexagonal axes)
[3] I4/mmm 2a 2b; 4c 8f 4d; 8j 4e; 8i 16m 8g; 2 × 8j
  (139) 8h; 16n 16k; 32o 16l; 2 × 16n 16m; 32o 3 × 32o
 conjugate: b, c, a y, z, x
 conjugate: c, a, b z, x, y
II Maximal klassengleiche subgroups
   Loss of centring translations
[2] Pn-3m origin 1: x, y, z 2a 6d 4b; 4c 12f 12g 2 × 8e 24h
  (224) origin 2: x + (1/4), y + (1/4), z + (1/4) 24k 24i; 24j 48l 2 × 24k 2 × 48l
[2] Pm-3n 2a 6b 8e 6c; 6d 12f 16i 12g; 12h
  (223) 24k 2 × 24j 2 × 24k 48l 2 × 48l
[2] Pn-3n origin 1: x, y, z 2a 6b 8c 12d 12e 16f 24g
  (222) origin 2: x + (1/4), y + (1/4), z + (1/4) 24h 48i 48i 48i 2 × 48i
[2] Pm-3m 1a; 1b 3c; 3d 8g 12h 6e; 6f 2 × 8g 2 × 12h
  (221) 12i; 12j 48n 24k; 24l 2 × 24m 2 × 48n
   Enlarged unit cell, isomorphic
[27] Im-3m 3a, 3b, 3c (1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); 2a; 12e; 6b; 12e; 8c; 16f; 12d; 24g; 48i 3 × 12e; 3 × 16f; 3 × 24g;
±(0, (1/3), 0); ±(0, 0, (1/3)); 16f; 24h 24g; 24h; 48i; 3 × 48j; 96l 3 × 48j; 6 × 48k; 96l 6 × 48j;
±(0, (1/3), (1/3)); ±((1/3), 0, (1/3)); 48j; 48k 3 × 48k 3 × 48k 3 × 96l
±((1/3), (1/3), 0); ±((1/3), 0, (2/3));
±((1/3), (2/3), 0); ±(0, (1/3), (2/3)); 3 × 24h; 3 × 48i; 9 × 48j; 9 × 48k; 27 × 96l
±((1/3), (1/3), (1/3)); ±((2/3), (1/3), (1/3)); 3 × 48j; 12 × 96l 9 × 96l 9 × 96l
±((1/3), (2/3), (1/3)); ±((1/3), (1/3), (2/3)) 3 × 48k;
3 × 96l


Axes Coordinates Wyckoff positions
2a 6b 8c 12d 12e 16f
24g 24h 48i 48j 48k 96l
[p3] Im-3m pa, pb, pc (1/p)x, (1/p)y, (1/p)z; 2a; ((p - 1)/2) × 12e; 6b; ((p - 1)/2) × 12e; 8c; ((p - 1)/2) × 16f; 12d; ((p - 1)/2) × 24g; p × 12e; p × 16f;
+((u/p), (v/p), (w/p)) ((p - 1)/2) × 16f; ((p - 1)/2) × 24g; ((p - 1)/2) × 48i; ((p - 1)/2) × 48i; ((p(p - 1))/2) × 48j; p(p - 1) × 48k;
p = prime > 2; ((p - 1)/2) × 24h; ((p - 1)/2) × 24h; ((p(p - 1))/2) × 48k; ((p(p - 1))/2) × 48j; ((p(p - 1))/2) × 48k; ((p(p - 1)(p - 2))/6) × 96l
u, v, w = 1, . . ., p - 1 (((p - 1)(p - 3))/8) × 48j; (((p - 1)(3p - 5))/8) × 48j; (((p2 - 1)(p - 3))/12) × 96l (((p2 - 1)(p - 2))/8) × 96l ((p(p - 1)(p - 3))/8) × 96l
(((p - 1)(p - 3))/4) × 48k; (((p - 1)2)/4) × 48k;
(((p - 1)(p - 3)(p - 5))/48) × (((p - 1)2(p - 3))/16) × 96l
96l
p × 24g; p × 24h; p × 48i; p2 × 48j; p2 × 48k; p3 × 96l
p(p - 1) × 48j; ((p(p - 1))/2) × 48j; ((p(p2 - 1))/2) × 96l ((p2(p - 1))/2) × 96l ((p2(p - 1))/2) × 96l
((p(p - 1)2)/4) × 96l ((p(p - 1))/2) × 48k;
((p(p - 1)2)/4) × 96l









































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