Pm-3n No. 223 P42/m-32/n Oh3


Axes Coordinates Wyckoff positions
2a 6b 6c 6d 8e 12f 12g
12h 16i 24j 24k 48l
I Maximal translationengleiche subgroups
[2] P-43n 2a 6b 6d 6c 8e 12f 12h
  (218) 12g 2 × 8e 24i 24i 2 × 24i
[2] P4232 2a 6d 6e 6f 4b; 4c 12h 12i
  (208) 12j 2 × 8g 12k; 12l 24m 2 × 24m
[2] Pm-3 1a; 1b 3c; 3d 6f 6g 8i 6e; 6h 2 × 6f
  (200) 2 × 6g 2 × 8i 24l 12j; 12k 2 × 24l
[4] R-3c (rhombohedral axes) 2b 6d 6e 6e 2a; 6e 12f 12f
  (167) 12f 4c; 12f 2 × 6e; 12f 2 × 12f 4 × 12f
a - b, b - c, (1/3)(2x - y - z), (1/3)(x + y - 2z), 6b 18d 18e 18e 6a; 18e 36f 36f
a + b + c (1/3)(x + y + z) 36f 12c; 36f 2 × 18e; 36f 2 × 36f 4 × 36f
(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] P42/mmc x + (1/2), y, z 2d 2a; 2b; 2c 2f; 4l 2e; 4m 8n 4i; 4j; 4k 4h; 2 × 4l
  (131) 4g; 2 × 4m 16r 8n; 16r 8o; 8p; 8q 3 × 16r
 conjugate: b, c, a y + (1/2), z, x
 conjugate: c, a, b z + (1/2), x, y
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[4] Ia-3d 2a, 2b, 2c (1/2)x, (1/2)y, (1/2)z; +((1/2), 0, 0); 16a 48f 24c; 24d 48g 16b; 48g 96h 2 × 48f
  (230) +(0, (1/2), 0); +(0, 0, (1/2)) 96h 32e; 96h 2 × 48g; 96h 2 × 96h 4 × 96h
[4] Ia-3d 2a, 2b, 2c (1/2)x + (1/4), (1/2)y + (1/4), (1/2)z + (1/4); 16a 48f 48g 24c; 24d 16b; 48g 96h 96h
  (230) +((1/2), 0, 0); +(0, (1/2), 0); 2 × 48f 32e; 96h 2 × 48g; 96h 2 × 96h 4 × 96h
+(0, 0, (1/2))
   Enlarged unit cell, isomorphic
[27] Pm-3n 3a, 3b, 3c (1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); 2a; 12f; 6b; 12f; 6c; 12g; 6d; 12h; 8e; 16i; 3 × 12f; 3 × 12g;
±(0, (1/3), 0); ±(0, 0, (1/3)); 16i; 24k 12g; 12h; 24j; 24j; 2 × 24j; 6 × 24k; 6 × 24k;
±(0, (1/3), (1/3)); ±((1/3), 0, (1/3)); 3 × 24k; 48l 3 × 24k; 48l 3 × 24k; 48l 3 × 48l 3 × 48l 3 × 48l
±((1/3), (1/3), 0); ±(0, (1/3), (2/3));
±((1/3), 0, (2/3)); ±((1/3), (2/3), 0); 3 × 12h; 3 × 16i; 3 × 24j; 9 × 24k; 27 × 48l
±((1/3), (1/3), (1/3)); ±((1/3), (1/3), (2/3)); 6 × 24k; 8 × 48l 12 × 48l 9 × 48l
±((1/3), (2/3), (1/3)); ±((2/3), (1/3), (1/3)) 3 × 48l


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









































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