P-62m No. 189 D3h3


Axes Coordinates Wyckoff positions
1a 1b 2c 2d 2e 3f
3g 4h 6i 6j 6k 12l
I Maximal translationengleiche subgroups
[2] P-6 (174) 1a 1b 1c; 1e 1d; 1f 2g 3j
3k 2h; 2i 6l 2 × 3j 2 × 3k 2 × 6l
[2] P31m 1a 1a 2b 2b 2 × 1a 3c
  (157) 3c 2 × 2b 2 × 3c 6d 6d 2 × 6d
[2] P321 1a 1b 2d 2d 2c 3e
  (150) 3f 2 × 2d 6g 6g 6g 2 × 6g
[3] Cm2m 2a + b, b, c (1/2)x, -(1/2)x + y, z 2a 2b 4d 4e 4c 2a; 4d
  (38) 2b; 4e 8f 4c; 8f 3 × 4d 3 × 4e 3 × 8f
 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
[conventional setting]Amm2 c, 2a + b, b z, (1/2)x, -(1/2)x + y
  or c, -a + b, -a - b z, (1/2)(-x + y), (1/2)(-x - y)
  or c, -a - 2b, a z, -(1/2)y, x - (1/2)y
 alternative:
C2mm a, a + 2b, c x - (1/2)y, (1/2)y, z
  or b, -2a - b, c -(1/2)x + y, -(1/2)x, z
  or -a - b, a - b, c -(1/2)(x + y), (1/2)(x - y), z
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] P-62c a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a 2b 4f 2c; 2d 4e 6g
  (190) 6h 2 × 4f 12i 12i 2 × 6h 2 × 12i
[2] P-62c a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 2b 2a 2c; 2d 4f 4e 6h
  (190) 6g 2 × 4f 12i 2 × 6h 12i 2 × 12i
[3] P-6m2 a - b, a + 2b, c (1/3)(2x - y), (1/3)(x + y), z; 1a; 1c; 1e 1b; 1d; 1f 6l 6m 2g; 2h; 2i 3 × 3j
  (187) ±((1/3), (2/3), 0) 3 × 3k 12o 3 × 6n 3 × 6l 3 × 6m 3 × 12o
   Enlarged unit cell, isomorphic
[2] P-62m a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 1a; 1b 2e 2c; 2d 4h 2 × 2e 3f; 3g
6i 2 × 4h 2 × 6i 6j; 6k 12l 2 × 12l
[2] P-62m a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 2e 1a; 1b 4h 2c; 2d 2 × 2e 6i
3f; 3g 2 × 4h 2 × 6i 12l 6j; 6k 2 × 12l
[3] P-62m a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 1a; 2e 1b; 2e 2c; 4h 2d; 4h 3 × 2e 3f; 6i
3g; 6i 3 × 4h 3 × 6i 6j; 12l 6k; 12l 3 × 12l
[p] P-62m a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 1a; ((p - 1)/2) × 2e 1b; ((p - 1)/2) × 2e 2c; ((p - 1)/2) × 4h 2d; ((p - 1)/2) × 4h p × 2e 3f; ((p - 1)/2) × 6i
p = prime > 2; u = 1, . . ., p - 1 3g; ((p - 1)/2) × 6i p × 4h p × 6i 6j; ((p - 1)/2) × 12l 6k; ((p - 1)/2) × 12l p × 12l
[4] P-62m 2a, 2b, c (1/2)x, (1/2)y, z; +((1/2), 0, 0); 1a; 3f 1b; 3g 2c; 6j 2d; 6k 2e; 6i 2 × 3f; 6j
+(0, (1/2), 0); +((1/2), (1/2), 0) 2 × 3g; 6k 4h; 12l 2 × 6i; 12l 4 × 6j 4 × 6k 4 × 12l
[p2] P-62m pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) 1a; (p - 1) × 3f; 1b; (p - 1) × 3g; 2c; ((p2 - 1)/3) × 6j 2d; ((p2 - 1)/3) × 6k 2e; (p - 1) × 6i; p × 3f;
p = prime ≠ 3; u, v = 1, . . ., p - 1 (((p - 1)(p - 2))/6) × 6j (((p - 1)(p - 2))/6) × 6k (((p - 1)(p - 2))/6) × 12l ((p(p - 1))/2) × 6j
p × 3g; 4h; ((p2 - 1)/3) × 12l p × 6i; p2 × 6j p2 × 6k p2 × 12l
((p(p - 1))/2) × 6k ((p(p - 1))/2) × 12l









































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