P3m1 No. 156 C3v1


Axes Coordinates Wyckoff positions
1a 1b 1c 3d 6e
I Maximal translationengleiche subgroups
[2] P3 (143) 1a 1b 1c 3d 2 × 3d
[3] C1m1 (8) 2a + b, b, c (1/2)x, -(1/2)x + y, z 2a 2a 2a 2a; 4b 3 × 4b
 conjugate: a - b, a + b, c (1/2)(x - y), (1/2)(x + y), z
 conjugate: a + 2b, -a, c (1/2)y, -x + (1/2)y, z
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] P3c1 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a 2b 2c 6d 2 × 6d
  (158)
[3] P31m 2a + b, -a + b, c (1/3)(x + y), (1/3)(-x + 2y), z; 1a; 2b 3c 3c 3c; 6d 3 × 6d
  (157) ±((2/3), (1/3), 0)
[3] P31m 2a + b, -a + b, c (1/3)(x + y) + (1/3), (1/3)(-x + 2y), z; 3c 1a; 2b 3c 3c; 6d 3 × 6d
  (157) ±((2/3), (1/3), 0)
[3] P31m 2a + b, -a + b, c (1/3)(x + y) - (1/3), (1/3)(-x + 2y), z; 3c 3c 1a; 2b 3c; 6d 3 × 6d
  (157) ±((2/3), (1/3), 0)
   Enlarged unit cell, isomorphic
[2] P3m1 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2 × 1a 2 × 1b 2 × 1c 2 × 3d 2 × 6e
[3] P3m1 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 3 × 1a 3 × 1b 3 × 1c 3 × 3d 3 × 6e
[p] P3m1 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) p × 1a p × 1b p × 1c p × 3d p × 6e
p = prime; u = 1, . . ., p - 1
[4] P3m1 2a, 2b, c (1/2)x, (1/2)y, z; +((1/2), 0, 0); 1a; 3d 1c; 3d 1b; 3d 2 × 3d; 6e 4 × 6e
+(0, (1/2), 0); +((1/2), (1/2), 0)
[p2] P3m1 pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) 1a; (p - 1) × 3d; 1b(c*); 1c(b*); p × 3d; p2 × 6e
p = prime ≠ 3; u, v = 1, . . ., p - 1 (((p - 1)(p - 2))/6) × 6e (p - 1) × 3d; (p - 1) × 3d; ((p(p - 1))/2) × 6e
(((p - 1)(p - 2))/6) × 6e (((p - 1)(p - 2))/6) × 6e
* p = 3n - 1










































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