|
Axes |
Coordinates |
Wyckoff positions |
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|
|
2a |
2b |
6c |
| I Maximal translationengleiche subgroups |
| [2] P3 (143) |
|
|
2 × 1a |
1b; 1c |
2 × 3d |
| [3] P1121 (4) |
|
|
2a |
2a |
3 × 2a |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, non-isomorphic |
| [3] P65 (170) |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
6a |
6a |
3 × 6a |
| [3] P61 (169) |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
6a |
6a |
3 × 6a |
| Enlarged unit cell, isomorphic |
| [3] P63 |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
3 × 2a |
3 × 2b |
3 × 6c |
| [p] P63 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
p × 2a |
p × 2b |
p × 6c |
|
p = prime > 2; u = 1, . . ., p - 1 |
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|
|
| [3] P63 |
2a + b, -a + b, c |
(1/3)(x + y), (1/3)(-x + 2y), z; ±((1/3), (2/3), 0) |
2a; 2 × 2b |
6c |
3 × 6c |
| [7] P63 |
3a + b, -a + 2b, c |
(1/7)(2x + y), (1/7)(-x + 3y), z; |
2a; 2 × 6c |
2b; 2 × 6c |
7 × 6c |
|
|
±((1/7), (3/7), 0); ±((3/7), (2/7), 0); ±((5/7), (1/7), 0) |
|
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|
| [7] P63 |
3a + 2b, -2a + b, c |
(1/7)(x + 2y), (1/7)(-2x + 3y), z; |
2a; 2 × 6c |
2b; 2 × 6c |
7 × 6c |
|
|
±((2/7), (3/7), 0); ±((3/7), (1/7), 0); ±((1/7), (5/7), 0) |
|
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|
| [p] P63 |
qa + rb, |
(1/p)((q - r)x + ry), (1/p)(-rx + qy), z; |
2a; ((p - 1)/3) × 6c |
2b; ((p - 1)/3) × 6c |
p × 6c |
|
-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] P63 |
2a, 2b, c |
(1/2)x, (1/2)y, z; +((1/2), 0, 0); |
2a; 6c |
2b; 6c |
4 × 6c |
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+(0, (1/2), 0); +((1/2), (1/2), 0) |
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|
| [p2] P63 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
2a; ((p2 - 1)/3) × 6c |
2b; ((p2 - 1)/3) × 6c |
p2 × 6c |
|
p = prime = 3n - 1; u, v = 1, . . ., p - 1 |
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