|
Axes |
Coordinates |
Wyckoff positions |
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2a |
2b |
2c |
2d |
4e |
4f |
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6g |
6h |
12i |
| I Maximal translationengleiche subgroups |
| [2] P31c (159) |
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2a |
2a |
2b |
2b |
2 × 2a |
2 × 2b |
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6c |
6c |
2 × 6c |
| [2] P312 (149) |
x, y, z + (1/4) |
1a; 1b |
2g |
1d; 1e |
1c; 1f |
2 × 2g |
2h; 2i |
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6l |
3j; 3k |
2 × 6l |
| [2] P-3 (147) |
|
2c |
1a; 1b |
2d |
2d |
2 × 2c |
2 × 2d |
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3e; 3f |
6g |
2 × 6g |
| [3] C12/c1 |
a, a + 2b, c |
x - (1/2)y, (1/2)y, z |
4e |
4a |
4e |
4e |
8f |
8f |
| (15) |
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4b; 4c; 4d |
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 |
-(x + y), (1/2)(x - y), z |
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| II Maximal klassengleiche subgroups |
| Enlarged unit cell, non-isomorphic |
| [3] P-3c1 |
2a + b, |
(1/3)(x + y), (1/3)(-x + 2y), z; |
2a; 4d |
2b; 4d |
6f |
6f |
4c; 2 × 4d |
12g |
| (165) |
-a + b, c |
±((1/3), (2/3), 0) |
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6e; 12g |
6f; 12g |
3 × 12g |
| [3] R-3c |
a - b, |
(1/3)(2x - y), (1/3)(x + y), (1/3)z; |
6a; 12c |
6b; 12c |
18e |
18e |
3 × 12c |
36f |
| (167) |
a + 2b, 3c |
±(0, 0, (1/3)) |
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18d; 36f |
18e; 36f |
3 × 36f |
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(hexagonal axes) |
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| [3] R-3c |
2a + b, |
(1/3)(x + y), (1/3)(-x + 2y), (1/3)z; |
6a; 12c |
6b; 12c |
18e |
18e |
3 × 12c |
36f |
| (167) |
-a + b, 3c |
±(0, 0, (1/3)) |
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18d; 36f |
18e; 36f |
3 × 36f |
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(hexagonal axes) |
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| Enlarged unit cell, isomorphic |
| [3] P-31c |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
2a; 4e |
2b; 4e |
2d; 4f |
2c; 4f |
3 × 4e |
3 × 4f |
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6g; 12i |
6h; 12i |
3 × 12i |
| [p] P-31c |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
2a; ((p - 1)/2) × 4e |
2b; ((p - 1)/2) × 4e |
2c(d*); ((p - 1)/2) × 4f |
2d(c*); ((p - 1)/2) × 4f |
p × 4e |
p × 4f |
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p = prime > 2; u = 1, . . ., p - 1 |
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6g; ((p - 1)/2) × 12i |
6h; ((p - 1)/2) × 12i |
p × 12i |
| [4] P-31c |
2a, 2b, c |
(1/2)x, (1/2)y, z; +((1/2), 0, 0); |
2a; 6h |
2b; 6g |
2d; 6h |
2c; 6h |
4e; 12i |
4f; 12i |
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+(0, (1/2), 0); +((1/2), (1/2), 0) |
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2 × 12i |
2 × 6h; 12i |
4 × 12i |
| [p2] P-31c |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
2a; |
2b; |
2c(d† ); |
2d(c† ); |
4e; |
4f; |
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p = prime > 4; |
(p - 1) × 6h; |
((p2 - 1)/6) × 12i |
(p - 1) × 6h; |
(p - 1) × 6h; |
((p2 - 1)/3) × 12i |
((p2 - 1)/3) × 12i |
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u, v = 1, . . ., p - 1 |
(((p - 1)(p - 2))/6) × 12i |
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(((p - 1)(p - 2))/6) × 12i |
(((p - 1)(p - 2))/6) × 12i |
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6g; ((p2 - 1)/2) × 12i |
p × 6h; |
p2 × 12i |
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((p(p - 1))/2) × 12i |
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| * p = 4n - 1 |
† p = 6n - 1 |
