Pm-3m No. 221 P4/m-32/m Oh1


Axes Coordinates Wyckoff positions
1a 1b 3c 3d 6e 6f 8g
12h 12i 12j 24k 24l 24m 48n
I Maximal translationengleiche subgroups
[2] P-43m 1a 1b 3c 3d 6f 6g 2 × 4e
  (215) 12h 12i 12i 24j 24j 2 × 12i 2 × 24j
[2] P432 1a 1b 3c 3d 6e 6f 8g
  (207) 12h 12i 12j 24k 24k 24k 2 × 24k
[2] Pm-3 1a 1b 3c 3d 6e 6h 8i
  (200) 6f; 6g 12j 12k 2 × 12j 2 × 12k 24l 2 × 24l
[4] R-3m (rhombohedral axes) 1a 1b 3e 3d 6h 6h 2c; 6h
  (166) 12i 6f; 6h 6g; 6h 2 × 12i 2 × 12i 2 × 6h; 12i 4 × 12i
a - b, b - c, (1/3)(2x - y - z), (1/3)(x + y - 2z), 3a 3b 9e 9d 18h 18h 6c; 18h
a + b + c (1/3)(x + y + z) 36i 18f; 18h 18g; 18h 2 × 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),
-a + b - c (1/3)(-x + y - z)
(hexagonal axes)
 conjugate: a + b, -b + c, (1/3)(2x + y + z), (1/3)(x - y + 2z),
a - b - c (1/3)(x - y - z)
(hexagonal axes)
 conjugate: -a + b, -b - c, (1/3)(-2x + y - z), (1/3)(-x - y - 2z),
-a - b + c (1/3)(-x - y + z)
(hexagonal axes)
[3] P4/mmm 1a 1d 1c; 2e 1b; 2f 2g; 4l 2h; 4o 8r
  (123) 4i; 4m; 4n 4j; 8s 4k; 8t 8p; 2 × 8s 8q; 2 × 8t 8r; 16u 3 × 16u
 conjugate: b, c, a y, z, x
 conjugate: c, a, b z, x, y
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] Fm-3c 2a, 2b, 2c (1/2)x, (1/2)y, (1/2)z; +((1/2), 0, 0) 8b 8a 24d 24c 48e 48f 64g
  (226) 96i 96i 96h 2 × 96i 192j 192j 2 × 192j
[2] Fm-3c 2a, 2b, 2c (1/2)x + (1/4), (1/2)y + (1/4), (1/2)z + (1/4); 8a 8b 24c 24d 48f 48e 64g
  (226) +((1/2), 0, 0) 96i 96h 96i 192j 2 × 96i 192j 2 × 192j
[2] Fm-3m 2a, 2b, 2c (1/2)x, (1/2)y, (1/2)z; +((1/2), 0, 0) 4a; 4b 8c 24d 24e 2 × 24e 48g 2 × 32f
  (225) 96j 24h; 48i 96k 2 × 96j 192l 2 × 96k 2 × 192l
[2] Fm-3m 2a, 2b, 2c (1/2)x + (1/4), (1/2)y + (1/4), (1/2)z + (1/4); 8c 4a; 4b 24e 24d 48g 2 × 24e 2 × 32f
  (225) +((1/2), 0, 0) 96j 96k 48h; 48i 192l 2 × 96j 2 × 96k 2 × 192l
[4] Im-3m 2a, 2b, 2c (1/2)x, (1/2)y, (1/2)z; +((1/2), 0, 0); 2a; 6b 8c 24h 12d; 12e 2 × 12e; 24g 48k 16f; 48k
  (229) +(0, (1/2), 0); +(0, 0, (1/2)) 2 × 48j 2 × 24h; 48j 48i; 48k 4 × 48j 2 × 96l 2 × 48k; 96l 4 × 96l
[4] Im-3m 2a, 2b, 2c (1/2)x + (1/4), (1/2)y + (1/4), (1/2)z + (1/4); 8c 2a; 6b 12d; 12e 24h 48k 2 × 12e; 24g 16f; 48k
  (229) ((1/2), 0, 0); +(0, (1/2), 0); 2 × 48j 48i; 48k 2 × 24h; 48j 2 × 96l 4 × 48j 2 × 48k; 96l 4 × 96l
+(0, 0, (1/2))


Axes Coordinates  Wyckoff positions
1a 1b 3c 3d 6e 6f
8g 12h 12i 12j 24k
24l 24m 48n
   Enlarged unit cell, isomorphic
[27] Pm-3m 3a, 3b, 3c (1/3)x, (1/3)y, (1/3)z; 1a; 6e; 8g; 12i 1b; 6f; 8g; 12j 3c; 6f; 12h; 12i; 3d; 6e; 12h; 3 × 6e; 3 × 24k; 3 × 6f; 3 × 24l;
±((1/3), 0, 0); 24l; 24m 12j; 24k; 24m 3 × 24m 3 × 24m
±(0, (1/3), 0);
±(0, 0, (1/3)); 3 × 8g; 6 × 24m; 3 × 12h; 3 × 24k; 3 × 12i; 3 × 24k; 3 × 12j; 3 × 24l; 9 × 24k;
±(0, (1/3), (1/3)); ±((1/3), 0, (1/3)); 48n 3 × 24l; 3 × 48n 3 × 24m; 3 × 24m; 9 × 48n
±((1/3), (1/3), 0); ±(0, (1/3), (2/3)); 3 × 48n 3 × 48n
±((1/3), 0, (2/3)); ±((1/3), (2/3), 0);
±((1/3), (1/3), (1/3)); ±((1/3), (1/3), (2/3)); 9 × 24l; 9 × 48n 9 × 24m; 27 × 48n
±((1/3), (2/3), (1/3)); ±((2/3), (1/3), (1/3)) 9 × 48n
[p3] Pm-3m pa, pb, pc (1/p)x, (1/p)y, (1/p)z; 1a; ((p - 1)/2) × 6e; 1b; ((p - 1)/2) × 6f; 3c; ((p - 1)/2) × 6f; 3d; ((p - 1)/2) × 6e; p × 6e; p × 6f;
+((u/p), (v/p), (w/p)) ((p - 1)/2) × 8g; ((p - 1)/2) × 8g; ((p - 1)/2) × 12h; ((p - 1)/2) × 12h; ((p(p - 1))/2) × 24k; ((p(p - 1))/2) × 24l;
p = prime > 2; ((p - 1)/2) × 12i; ((p - 1)/2) × 12j; ((p - 1)/2) × 12i; ((p - 1)/2) × 12j; ((p(p - 1))/2) × 24m; ((p(p - 1))/2) × 24m;
u, v, w = 1, . . ., p - 1 (((p - 1)(p - 3))/8) × 24k; (((p - 1)(p - 3))/8) × 24l; (((p - 1)(p - 3))/8) × 24k; (((p - 1)2)/4) × 24k; ((p(p - 1)(p - 3))/8) × ((p(p - 1)(p - 3))/8) ×
(((p - 1)(p - 3))/4) × 24m; (((p - 1)(p - 3))/4) × (((p - 1)2)/4) × 24l; (((p - 1)(p - 3))/8) × 24l; 48n 48n
(((p - 1)(p - 3)(p - 5))/48) × 24m; (((p - 1)2)/4) × 24m; (((p - 1)2)/4) × 24m;
48n (((p - 1)(p - 3)(p - 5))/48) × (((p - 1)2(p - 3))/16) × (((p - 1)2(p - 3))/16) ×
48n 48n 48n
p × 8g; p × 12h; p × 12i; p × 12j; p2 × 24k;
p(p - 1) × 24m; ((p(p - 1))/2) × 24k; ((p(p - 1))/2) × 24k; ((p(p - 1))/2) × 24l; ((p2(p - 1))/2) × 48n
((p(p - 1)(p - 2))/6) × ((p(p - 1))/2) × 24l; ((p(p - 1))/2) × 24m; ((p(p - 1))/2) × 24m;
48n ((p(p - 1)2)/4) × 48n ((p(p - 1)2)/4) × 48n ((p(p - 1)2)/4) × 48n
p2 × 24l; p2 × 24m; p3 × 48n
((p2(p - 1))/2) × 48n ((p2(p - 1))/2) × 48n









































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