|
Axes |
Coordinates |
Wyckoff positions |
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1a |
2b |
3c |
6d |
| I Maximal translationengleiche subgroups |
| [2] P3 (143) |
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1a |
1b; 1c |
3d |
2 × 3d |
| [3] P112 (3) |
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1a |
2e |
1b; 1c; 1d |
3 × 2e |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, non-isomorphic |
| [2] P63 (173) |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
2a |
2 × 2b |
6c |
2 × 6c |
| [3] P64 (172) |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
3a |
6c |
3 × 3b |
3 × 6c |
| [3] P62 (171) |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
3a |
6c |
3 × 3b |
3 × 6c |
| Enlarged unit cell, isomorphic |
| [2] P6 |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
2 × 1a |
2 × 2b |
2 × 3c |
2 × 6d |
| [3] P6 |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
3 × 1a |
3 × 2b |
3 × 3c |
3 × 6d |
| [p] P6 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
p × 1a |
p × 2b |
p × 3c |
p × 6d |
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p = prime; u = 1, . . ., p - 1 |
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| [3] P6 |
2a + b, -a + b, c |
(1/3)(x + y), (1/3)(-x + 2y), z; ±((1/3), (2/3), 0) |
1a; 2b |
6d |
3c; 6d |
3 × 6d |
| [7] P6 |
3a + b, -a + 2b, c |
(1/7)(2x + y), (1/7)(-x + 3y), z; ±((1/7), (3/7), 0); |
1a; 6d |
2b; 2 × 6d |
3c; 3 × 6d |
7 × 6d |
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±((3/7), (2/7), 0); ±((5/7), (1/7), 0) |
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| [7] P6 |
3a + 2b, -2a + b, c |
(1/7)(x + 2y), (1/7)(-2x + 3y), z; ±((2/7), (3/7), 0); |
1a; 6d |
2b; 2 × 6d |
3c; 3 × 6d |
7 × 6d |
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±((3/7), (1/7), 0); ±((1/7), (5/7), 0) |
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| [p] P6 |
qa + rb, |
(1/p)((q - r)x + ry), (1/p)(-rx + qy), z; |
1a; ((p - 1)/6) × 6d |
2b; ((p - 1)/3) × 6d |
3c; ((p - 1)/2) × 6d |
p × 6d |
|
-ra +(q - r)b, c |
+((ur/p), (uq/p), 0) |
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p = prime = q2 - qr + r2 = 6n + 1; |
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q, r = 1, 2, . . .; q> r; u = 1, . . ., p - 1 |
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| [4] P6 |
2a, 2b, c |
(1/2)x, (1/2)y, z; +((1/2), 0, 0); +(0, (1/2), 0); +((1/2), (1/2), 0) |
1a; 3c |
2b; 6d |
2 × 6d |
4 × 6d |
| [p2] P6 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
1a; ((p2 - 1)/6) × 6d |
2b; ((p2 - 1)/3) × 6d |
3c; ((p2 - 1)/2) × 6d |
p2 × 6d |
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p = prime = 6n - 1; u, v = 1, . . ., p - 1 |
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