P6/m No. 175 C6h1


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] P6 (168) 1a 1a 2b 2b 2 × 1a 3c 3c
2 × 2b 2 × 3c 6d 6d 2 × 6d
[2] P-3 (147) 1a 1b 2d 2d 2c 3e 3f
2 × 2d 6g 6g 6g 2 × 6g
[3] P112/m 1a 1b 2m 2n 2i 1c; 1d; 1g 1e; 1f; 1h
  (10) 4o 2j; 2k; 2l 3 × 2m 3 × 2n 3 × 4o
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] P63/m a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2b 2a 4f 2c; 2d 4e 6g 6h
  (176) 2 × 4f 12i 12i 2 × 6h 2 × 12i
[2] P63/m a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 2a 2b 2c; 2d 4f 4e 6h 6g
  (176) 2 × 4f 12i 2 × 6h 12i 2 × 12i
   Enlarged unit cell, isomorphic
[2] P6/m 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] P6/m 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] P6/m 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] P6/m a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 1a; 1b; 2c; 2d; p × 2e 3f; 3g;
p = prime > 2; u = 1, . . ., p - 1 ((p - 1)/2) × 2e ((p - 1)/2) × 2e ((p - 1)/2) × 4h ((p - 1)/2) × 4h ((p - 1)/2) × 6i ((p - 1)/2) × 6i
p × 4h p × 6i 6j; 6k; p × 12l
((p - 1)/2) × 12l ((p - 1)/2) × 6l
[3] P6/m 2a + b, (1/3)(x + y), (1/3)(-x + 2y), z; 1a; 2c 1b; 2d 6j 6k 2e; 4h 3f; 6j 3g; 6k
-a + b, c ±((2/3), (1/3), 0) 12l 6i; 12l 3 × 6j 3 × 6k 3 × 12l
[7] P6/m 3a + b, (1/7)(2x + y), (1/7)(-x + 3y), z; 1a; 6j 1b; 6k 2c; 2 × 6j 2d; 2 × 6k 2e; 12l 3f; 3 × 6j 3g; 3 × 6k
-a + 2b, c ±((1/7), (3/7), 0); ±((3/7), (2/7), 0); ±((5/7), (1/7), 0) 4h; 2 × 12l 6i; 3 × 12l 7 × 6j 7 × 6k 7 × 12l
[7] P6/m 3a + 2b, (1/7)(x + 2y), (1/7)(-2x + 3y), z; 1a; 6j 1b; 6k 2c; 2 × 6j 2d; 2 × 6k 2e; 12l 3f; 3 × 6j 3g; 3 × 6k
-2a + b, c ±((2/7), (3/7), 0); ±((3/7), (1/7), 0); ±((1/7), (5/7), 0) 4h; 2 × 12l 6i; 3 × 12l 7 × 6j 7 × 6k 7 × 12l
[p] P6/m qa + rb, (1/p)((q - r)x + ry), 1a; 1b; 2c; 2d; 2e; 3f; 3g;
-ra +(q - r)b, c (1/p)(-rx + qy), z; +((ur/p), (uq/p), 0) ((p - 1)/6) × 6j ((p - 1)/6) × 6k ((p - 1)/3) × 6j ((p - 1)/3) × 6k ((p - 1)/6) × 12l ((p - 1)/2) × 6j ((p - 1)/2) × 6k
p = q2 - qr + r2 = prime = 6n + 1; 4h; 6i; p × 6j p × 6k p × 12l
q, r = 1, 2, . . .; q> r; u = 1, . . ., p - 1 ((p - 1)/3) × 12l ((p - 1)/2) × 12l
[4] P6/m 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 × 6j 2 × 6k
+(0, (1/2), 0); +((1/2), (1/2), 0) 4h; 12l 2 × 12l 4 × 6j 4 × 6k 4 × 12l
[p2] P6/m pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) 1a; 1b; 2c; 2d; 2e; 3f; 3g;
p = prime = 6n - 1; u, v = 1, . . ., p - 1 ((p2 - 1)/6) × 6j ((p2 - 1)/6) × 6k ((p2 - 1)/3) × 6j ((p2 - 1)/3) × 6k ((p2 - 1)/6) × 12l ((p2 - 1)/2) × 6j ((p2 - 1)/2) × 6k
4h; 6i; p2 × 6j p2 × 6k p2 × 12l
((p2 - 1)/3) × 12l ((p2 - 1)/2) × 12l









































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