P6422 No. 181 D65


Axes Coordinates Wyckoff positions
3a 3b 3c 3d 6e 6f
6g 6h 6i 6j 12k
I Maximal translationengleiche subgroups
[2] P64 (172) 3a 3a 3b 3b 2 × 3a 2 × 3b
6c 6c 6c 6c 2 × 6c
[2] P3121 x, y, z + (1/3) 3a 3b 3a 3b 6c 6c
  (152) 2 × 3a 2 × 3b 6c 6c 2 × 6c
[2] P3112 x, y, z - (1/3) 3a 3b 3a 3b 6c 6c
  (151) 6c 6c 2 × 3a 2 × 3b 2 × 6c
[3] C222 a, a + 2b, c x - (1/2)y, (1/2)y, z 2a; 4i 2d; 4i 2b; 4k 2c; 4k 3 × 4i 4j; 2 × 4k
  (21) 4e; 8l 4f; 8l 4g; 8l 4h; 8l 3 × 8l
 conjugate: b, -2a - b, c -(1/2)x + y, -(1/2)x, z - (1/3)
 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
[2] P6522 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 6a 6b 6a 6b 12c 12c
  (179) 2 × 6a 12c 12c 2 × 6b 2 × 12c
[2] P6522 a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 6b 6a 6b 6a 12c 12c
  (179) 12c 2 × 6a 2 × 6b 12c 2 × 12c
   Enlarged unit cell, isomorphic
[2] P6222 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 3a; 3b 6e 3c; 3d 6f 2 × 6e 2 × 6f
  (180) 6g; 6h 12k 6i; 6j 12k 2 × 12k
[2] P6222 a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 6e 3a; 3b 6f 3c; 3d 2 × 6e 2 × 6f
  (180) 12k 6g; 6h 12k 6i; 6j 2 × 12k
[5] P6222 a, b, 5c x, y, (1/5)z; ±(0, 0, (1/5)); 3a; 2 × 6e 3b; 2 × 6e 3c; 2 × 6f 3d; 2 × 6f 5 × 6e 5 × 6f
  (180) ±(0, 0, (2/5)) 6g; 2 × 12k 6h; 2 × 12k 6i; 2 × 12k 6j; 2 × 12k 5 × 12k
[p] P6222 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 3a; ((p - 1)/2) × 6e 3b; ((p - 1)/2) × 6e 3c; ((p - 1)/2) × 6f 3d; ((p - 1)/2) × 6f p × 6e p × 6f
  (180) p = prime = 6n - 1; u = 1, . . ., p - 1 6g; ((p - 1)/2) × 12k 6h; ((p - 1)/2) × 12k 6i; ((p - 1)/2) × 12k 6j; ((p - 1)/2) × 12k p × 12k
[7] P6422 a, b, 7c x, y, (1/7) z; ±(0, 0, (1/7)) 3a; 3 × 6e 3b; 3 × 6e 3c; 3 × 6f 3d; 3 × 6f 7 × 6e 7 × 6f
±(0, 0, (2/7)); ±(0, 0, (3/7)) 6g; 3 × 12k 6h; 3 × 12k 6i; 3 × 12k 6j; 3 × 12k 7 × 12k
[p] P6422 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 3a; ((p - 1)/2) × 6e 3b; ((p - 1)/2) × 6e 3c; ((p - 1)/2) × 6f 3d; ((p - 1)/2) × 6f p × 6e p × 6f
p = prime = 6n + 1; u = 1, . . ., p - 1 6g; ((p - 1)/2) × 12k 6h; ((p - 1)/2) × 12k 6i; ((p - 1)/2) × 12k 6j; ((p - 1)/2) × 12k p × 12k
[3] P6422 2a + b, (1/3)(x + y), (1/3)(-x + 2y), 3a; 6i 3b; 6j 3c; 6i 3d; 6j 6e; 12k 6f; 12k
-a + b, c z - (1/3); ±((1/3), (2/3), 0) 3 × 6i 3 × 6j 6g; 12k 6h; 12k 3 × 12k
[4] P6422 2a, 2b, c (1/2)x, (1/2)y, z; +((1/2), 0, 0); 3a; 3c; 6f 3b; 3d; 6f 6g; 6i 6h; 6j 6e; 3 × 6f 2 × 12k
+(0, (1/2), 0); +((1/2), (1/2), 0) 2 × 6g; 12k 2 × 6h; 12k 2 × 6i; 12k 2 × 6j; 12k 4 × 12k
[p2] P6422 pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) 3a; ((p - 1)/2) × 6g; 3b; ((p - 1)/2) × 6h; 3c; ((p - 1)/2) × 6g; 3d; ((p - 1)/2) × 6h; 6e; ((p2 - 1)/2) × 12k 6f; ((p2 - 1)/2) × 12k
p = prime > 4; ((p - 1)/2) × 6i; ((p - 1)/2) × 6j; ((p - 1)/2) × 6i; ((p - 1)/2) × 6j;
u, v = 1, . . ., p - 1 (((p - 1)2)/4) × 12k (((p - 1)2)/4) × 12k (((p - 1)2)/4) × 12k (((p - 1)2)/4) × 12k
p × 6g; p × 6h; p × 6i; p × 6j; p2 × 12k
((p(p - 1))/2) × 12k ((p(p - 1))/2) × 12k ((p(p - 1))/2) × 12k ((p(p - 1))/2) × 12k










































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