P6mm No. 183 C6v1

 Axes Coordinates Wyckoff positions 1a 2b 3c 6d 6e 12f I Maximal translationengleiche subgroups [2] P6 (168) 1a 2b 3c 6d 6d 2 × 6d [2] P31m (157) 1a 2b 3c 2 × 3c 6d 2 × 6d [2] P3m1 (156) 1a 1b; 1c 3d 6e 2 × 3d 2 × 6e [3] Cmm2 (35) a, a + 2b, c x - (1/2)y, (1/2)y, z 2a 4e 2b; 4c 4d; 8f 4e; 8f 3 × 8f 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 alternative: Cmm2 2a + b, b, c (1/2)x, -(1/2)x + y, z 2a 4d 2b; 4c 4e; 8f 4d; 8f 3 × 8f or a + 2b, -a, c (1/2)y, -x + (1/2)y, 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] P63mc(186) a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a 2 × 2b 6c 12d 2 × 6c 2 × 12d [2] P63cm(185) a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a 4b 6c 2 × 6c 12d 2 × 12d [2] P6cc (184) a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a 4b 6c 12d 12d 2 × 12d Enlarged unit cell, isomorphic [2] P6mm a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2 × 1a 2 × 2b 2 × 3c 2 × 6d 2 × 6e 2 × 12f [3] P6mm a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 3 × 1a 3 × 2b 3 × 3c 3 × 6d 3 × 6e 3 × 12f [p] P6mm a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) p × 1a p × 2b p × 3c p × 6d p × 6e p × 12f p = prime; u = 1, . . ., p - 1 [3] P6mm 2a + b, (1/3)(x + y), (1/3)(-x + 2y), z + (1/3); 1a; 2b 6d 3c; 6e 3 × 6e 6d; 12f 3 × 12f -a + b, c ±((1/3), (2/3), 0) [4] P6mm 2a, 2b, c (1/2)x, (1/2)y, z; +((1/2), 0, 0); 1a; 3c 2b; 6e 6d; 6e 2 × 6d; 12f 2 × 6e; 12f 4 × 12f +(0, (1/2), 0); +((1/2), (1/2), 0) [p2] P6mm pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) 1a; ((p - 1)/2) × 6d; 2b; 3c; ((p - 1)/2) × 6d; p × 6d; p × 6e; p2 × 12f p = prime > 4; ((p - 1)/2) × 6e; (p - 1) × 6e; ((p - 1)/2) × 6e; ((p(p - 1))/2) × 12f ((p(p - 1))/2) × 12f u, v = 1, . . ., p - 1 (((p - 1)(p - 5))/12) × (((p - 1)(p - 2))/6) × (((p - 1)2)/4) × 12f 12f 12f