|
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] P-6 (174) |
|
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] P63 (173) |
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2a |
2a |
2b |
2b |
2 × 2a |
2 × 2b |
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6c |
6c |
2 × 6c |
| [2] P-3 (147) |
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2c |
1a; 1b |
2d |
2d |
2 × 2c |
2 × 2d |
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3e; 3f |
6g |
2 × 6g |
| [3] P1121/m |
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2e |
2a |
2e |
2e |
4f |
4f |
| (11) |
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2b; 2c; 2d |
3 × 2e |
3 × 4f |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, isomorphic |
| [3] P63/m |
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] P63/m |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
2a; |
2b; |
2c(d*); |
2d(c*); |
p × 4e |
p × 4f |
|
p = prime > 2; u = 1, . . ., p - 1 |
((p - 1)/2) × 4e |
((p - 1)/2) × 4e |
((p - 1)/2) × 4f |
((p - 1)/2) × 4f |
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6g; |
6h; |
p × 12i |
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((p - 1)/2) × 12i |
((p - 1)/2) × 12i |
|
| [3] P63/m |
2a + b, -a + b, c |
(1/3)(x + y), (1/3)(-x + 2y), z; ±((1/3), (2/3), 0) |
2a; 2c; 2d |
2b; 4f |
6h |
6h |
4e; 2 × 4f |
12i |
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6g; 12i |
3 × 6h |
3 × 12i |
| [7] P63/m |
3a + b, |
(1/7)(2x + y), (1/7)(-x + 3y), z; |
2a; 2 × 6h |
2b; 12i |
2c; 2 × 6h |
2d; 2 × 6h |
4e; 2 × 12i |
4f; 2 × 12i |
|
-a + 2b, c |
±((1/7), (3/7), 0); ±((3/7), (2/7), 0); ±((5/7), (1/7), 0) |
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6g; 3 × 12i |
7 × 6h |
7 × 12i |
| [7] P63/m |
3a + 2b, |
(1/7)(x + 2y), (1/7)(-2x + 3y), z; |
2a; 2 × 6h |
2b; 12i |
2d; 2 × 6h |
2c; 2 × 6h |
4e; 2 × 12i |
4f; 2 × 12i |
|
-2a + b, c |
±((2/7), (3/7), 0); ±((3/7), (1/7), 0); ±((1/7), (5/7), 0) |
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6g; 3 × 12i |
7 × 6h |
7 × 12i |
| [p] P63/m |
qa + rb, |
(1/p)((q - r)x + ry), |
2a; |
2b; |
2c(d† ); |
2d(c† ); |
4e; |
4f; |
|
-ra +(q - r)b, c |
(1/p)(-rx + qy), z; +((ur/p), (uq/p), 0) |
((p - 1)/3) × 6h |
((p - 1)/6) × 12i |
((p - 1)/3) × 6h |
((p - 1)/3) × 6h |
((p - 1)/3) × 12i |
((p - 1)/3) × 12i |
|
p = prime = q2 - qr + r2 = 6n + 1; |
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6g; |
p × 6h |
p × 12i |
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q, r = 1, 2, . . .; q> r; u = 1, . . ., p - 1 |
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((p - 1)/2) × 12i |
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| [4] P63/m |
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 |
4 × 6h |
4 × 12i |
| [p2] P63/m |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
2a; |
2b; |
2d; |
2c; |
4e; |
4f; |
|
p = prime = 6n - 1; u, v = 1, . . ., p - 1 |
((p2 - 1)/3) × 6h |
((p2 - 1)/6) × 12i |
((p2 - 1)/3) × 6h |
((p2 - 1)/3) × 6h |
((p2 - 1)/3) × 12i |
((p2 - 1)/3) × 12i |
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6g; |
p2 × 6h |
p2 × 12i |
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((p2 - 1)/2) × 12i |
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| * p = 4n - 1 |
† q + r = 3n - 1 |
