|
Axes |
Coordinates |
Wyckoff positions |
|
|
|
6a |
6b |
12c |
| I Maximal translationengleiche subgroups |
| [2] P61 (169) |
|
|
6a |
6a |
2 × 6a |
| [2] P3121 (152) |
|
x, y, z - (1/6) |
3a; 3b |
6c |
2 × 6c |
| [2] P3112 (151) |
|
x, y, z - (1/12) |
6c |
3a; 3b |
2 × 6c |
| [3] C2221 (20) |
a, a + 2b, c |
x - (1/2)y, (1/2)y, z |
4a; 8c |
4b; 8c |
3 × 8c |
| conjugate: |
b, -2a - b, c |
-(1/2)x + y, -(1/2)x, z + (1/6) |
|
|
|
| conjugate: |
-a - b, a - b, c |
-(1/2)(x + y), (1/2)(x - y), z - (1/6) |
|
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|
| alternative: |
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|
|
| C2221 |
2a + b, b, c |
(1/2)x, -(1/2)x + y, z - (1/12) |
4b; 8c |
4a; 8c |
3 × 8c |
| or |
a + 2b, -a, c |
(1/2)y, -x + (1/2)y, z - (1/4) |
|
|
|
| or |
a - b, a + b, c |
(1/2)(x - y), (1/2)(x + y), z + (1/12) |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, isomorphic |
| [5] P6522 (179) |
a, b, 5c |
x, y, (1/5)z; |
6a; 2 × 12c |
6b; 2 × 12c |
5 × 12c |
|
|
±(0, 0, (1/5)); ±(0, 0, (2/5)) |
|
|
|
| [p] P6522 (179) |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
6a; ((p - 1)/2) × 12c |
6b; ((p - 1)/2) × 12c |
p × 12c |
|
p = prime = 6n - 1; u = 1, . . ., p - 1 |
|
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|
| [7] P6122 |
a, b, 7c |
x, y, (1/7)z; ±(0, 0, (1/7)); |
6a; 3 × 12c |
6b; 3 × 12c |
7 × 12c |
|
|
±(0, 0, (2/7)); ±(0, 0, (3/7)) |
|
|
|
| [p] P6122 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
6a; ((p - 1)/2) × 12c |
6b; ((p - 1)/2) × 12c |
p × 12c |
|
p = prime = 6n + 1; u = 1, . . ., p - 1 |
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|
| [3] P6122 |
2a + b, -a + b, c |
(1/3)(x + y), (1/3)(-x + 2y), z - (1/12); |
3 × 6b |
6a; 12c |
3 × 12c |
|
|
±((1/3), (2/3), 0) |
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|
| [4] P6122 |
2a, 2b, c |
(1/2)x, (1/2)y, z; +((1/2), 0, 0); |
2 × 6a; 12c |
2 × 6b; 12c |
4 × 12c |
|
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+(0, (1/2), 0); +((1/2), (1/2), 0) |
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|
| [p2] P6122 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
p × 6a; ((p(p - 1))/2) × 12c |
p × 6b; ((p(p - 1))/2) × 12c |
p2 × 12c |
|
p = prime ≠ 3; u, v = 1, . . ., p - 1 |
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