P3212 No. 153 D35


Axes Coordinates Wyckoff positions
3a 3b 6c
I Maximal translationengleiche subgroups
[2] P32 (145) 3a 3a 2 × 3a
[3] C121 (5) a, a+2b, c x - (1/2)y, (1/2)y, z - (1/3) 2a; 4c 2b; 4c 3 × 4c
 conjugate: b, -2a - b, c -(1/2)x + y, -(1/2)x, z
 conjugate: -a - b, a - b, c (1/2)(-x - y), (1/2)(x - y), z + (1/3)
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[3] P3221 (154) a - b, a + 2b, c (1/3)(2x - y), (1/3)(x + y), z; ±((1/3), (2/3), 0) 3a; 6c 3b; 6c 3 × 6c
[3] P3221 (154) a - b, a + 2b, c (1/3)(2x - y) - (1/3), (1/3)(x + y), z; ±((1/3), (2/3), 0) 3a; 6c 3b; 6c 3 × 6c
[3] P3221 (154) a - b, a + 2b, c (1/3)(2x - y) + (1/3), (1/3)(x + y), z; ±((1/3), (2/3), 0) 3a; 6c 3b; 6c 3 × 6c
   Enlarged unit cell, isomorphic
[2] P3112 (151) a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 3a; 3b 6c 2 × 6c
[2] P3112 (151) a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 6c 3a; 3b 2 × 6c
[5] P3112 (151) a, b, 5c x, y, (1/5) z; ±(0, 0, (1/5)); ±(0, 0, (2/5)) 3a; 2 × 6c 3b; 2 × 6c 5 × 6c
[p] P3112 (151) a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 3a; ((p - 1)/2) × 6c 3b; ((p - 1)/2) × 6c p × 6c
p = prime = 6n - 1; u = 1, . . ., p - 1
[7] P3212 a, b, 7c x, y, (1/7) z; ±(0, 0, (1/7)); ±(0, 0, (2/7)); ±(0, 0, (3/7)) 3a; 3 × 6c 3b; 3 × 6c 7 × 6c
[p] P3212 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 3a; ((p - 1)/2) × 6c 3b; ((p - 1)/2) × 6c p × 6c
p = prime = 6n + 1; u = 1, . . ., p - 1
[4] P3212 2a, 2b, c (1/2)x, (1/2)y, z; +((1/2), 0, 0); +(0, (1/2), 0); +((1/2), (1/2), 0) 2 × 3a; 6c 2 × 3b; 6c 4 × 6c
[p2] P3212 pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) p × 3a; ((p(p - 1))/2) × 6c p × 3b; ((p(p - 1))/2) × 6c p2 × 6c
p = prime ≠ 3; u, v = 1, . . ., p - 1










































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