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Axes |
Coordinates |
Wyckoff positions |
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1a |
2b |
3c |
6d |
6e |
12f |
| I Maximal translationengleiche subgroups |
| [2] P6 (168) |
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1a |
2b |
3c |
6d |
6d |
2 × 6d |
| [2] P31m (157) |
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1a |
2b |
3c |
2 × 3c |
6d |
2 × 6d |
| [2] P3m1 (156) |
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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 |
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| conjugate: |
-a - b, a - b, c |
-(1/2)(x + y), (1/2)(x - y), z |
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| alternative: |
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| 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 |
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| or |
a - b, a + b, c |
(1/2)(x - y), (1/2)(x + y), z |
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| 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 |
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p = prime; u = 1, . . ., p - 1 |
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| [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 |
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-a + b, c |
±((1/3), (2/3), 0) |
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| [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 |
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+(0, (1/2), 0); +((1/2), (1/2), 0) |
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| [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 |
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p = prime > 4; |
((p - 1)/2) × 6e; |
(p - 1) × 6e; |
((p - 1)/2) × 6e; |
((p(p - 1))/2) × 12f |
((p(p - 1))/2) × 12f |
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u, v = 1, . . ., p - 1 |
(((p - 1)(p - 5))/12) × |
(((p - 1)(p - 2))/6) × |
(((p - 1)2)/4) × 12f |
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12f |
12f |
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