Pm-3 No. 200 P2/m-3 Th1


Axes Coordinates Wyckoff positions
1a 1b 3c 3d 6e 6f 6g
6h 8i 12j 12k 24l
I Maximal translationengleiche subgroups
[2] P23 1a 1b 3c 3d 6f 6g 6h
  (195) 6i 2 × 4e 12j 12j 2 × 12j
[4] R-3 (rhombohedral axes) 1a 1b 3e 3d 6f 6f 6f
  (148) 6f 2c; 6f 2 × 6f 2 × 6f 4 × 6f
a - b, b - c, (1/3)(2x - y - z), 3a 3b 9e 9d 18f 18f 18f
a + b + c (1/3)(x + y - 2z), 18f 6c; 18f 2 × 18f 2 × 18f 4 × 18f
(hexagonal axes) (1/3)(x + y + z)
 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] Pmmm 1a 1h 1d; 1f; 1g 1b; 1c; 1e 2i; 2m; 2q 2j; 2o; 2r 2k; 2n; 2s
  (47) 2l; 2p; 2t 8[alpha] 4u; 4w; 4y 4v; 4x; 4z 3 × 8[alpha]
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] Fm-3 2a, 2b, 2c (1/2)x, (1/2)y, (1/2)z; +((1/2), 0, 0) 4a; 4b 8c 24d 24e 2 × 24e 48h 48h
  (202) 48g 2 × 32f 2 × 48h 96i 2 × 96i
[2] Fm-3 2a, 2b, 2c (1/2)x + (1/4), (1/2)y + (1/4), (1/2)z + (1/4); 8c 4a; 4b 24e 24d 48g 48h 48h
  (202) +((1/2), 0, 0) 2 × 24e 2 × 32f 96i 2 × 48h 2 × 96i
[4] Ia-3 2a, 2b, 2c (1/2)x, (1/2)y, (1/2)z; +((1/2), 0, 0); 8a 8b 24d 24d 48e 2 × 24d 48e
  (206) +(0, (1/2), 0); +(0, 0, (1/2)) 48e 16c; 48e 2 × 48e 2 × 48e 4 × 48e
[4] Ia-3 2a, 2b, 2c (1/2)x + (1/4), (1/2)y + (1/4), (1/2)z + (1/4); +((1/2), 0, 0); 8b 8a 24d 24d 48e 48e 2 × 24d
  (206) +(0, (1/2), 0); +(0, 0, (1/2)) 48e 16c; 48e 2 × 48e 2 × 48e 4 × 48e
[4] Im-3 2a, 2b, 2c (1/2)x, (1/2)y, (1/2)z; +((1/2), 0, 0); 2a; 6b 8c 24g 12d; 12e 2 × 12d; 2 × 12e 2 × 24g 2 × 24g
  (204) +(0, (1/2), 0); +(0, 0, (1/2)) 48h 16f; 48h 4 × 24g 2 × 48h 4 × 48h
[4] Im-3 2a, 2b, 2c (1/2)x + (1/4), (1/2)y + (1/4), (1/2)z + (1/4); +((1/2), 0, 0); 8c 2a; 6b 12d; 12e 24g 48h 2 × 24g 2 × 24g
  (204) +(0, (1/2), 0); +(0, 0, (1/2)) 2 × 12d; 2 × 12e 16f; 48h 2 × 48h 4 × 24g 4 × 48h


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









































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