| P62 |
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P64 |
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Axes |
Coordinates |
Wyckoff positions |
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Axes |
Coordinates |
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3a |
3b |
6c |
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| I Maximal translationengleiche subgroups |
| [2] P32 (145) |
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3a |
3a |
3 × 3a |
[2] P31 (144) |
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| [3] P112 (3) |
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3 × 1a |
1b; 1c; 1d |
3 × 2e |
[3] P112 (3) |
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| II Maximal klassengleiche subgroups |
| Enlarged unit cell, non-isomorphic |
| [2] P61 |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
6a |
6a |
2 × 6a |
[2] P65 |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
| (169) |
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(170) |
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| Enlarged unit cell, isomorphic |
| [2] P64 |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
2 × 3a |
2 × 3b |
2 × 6c |
[2] P62 |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
| (172) |
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(171) |
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| [5] P64 |
a, b, 5c |
x, y, (1/5) z; ±(0, 0, (1/5)); |
5 × 3a |
5 × 3b |
5 × 6c |
[5] P62 |
a, b, 5c |
x, y, (1/5) z; ±(0, 0, (1/5)); |
| (172) |
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±(0, 0, (2/5)) |
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(171) |
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±(0, 0, (2/5)) |
| [p] P64 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
p × 3a |
p × 3b |
p × 6c |
[p] P62 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
| (172) |
p = prime = 3n - 1; u = 1, . . ., p - 1 |
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(171) |
p = prime = 3n - 1; u = 1, . . ., p - 1 |
| [7] P62 |
a, b, 7c |
x, y, (1/7) z; ±(0, 0, (1/7)); |
7 × 3a |
7 × 3b |
7 × 6c |
[7] P64 |
a, b, 7c |
x, y, (1/7) z; ±(0, 0, (1/7)); |
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±(0, 0, (2/7)); ±(0, 0, (3/7)) |
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±(0, 0, (2/7)); ±(0, 0, (3/7)) |
| [p] P62 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
p × 3a |
p × 3b |
p × 6c |
[p] P64 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
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p = prime = 6n + 1; u = 1, . . ., p - 1 |
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p = prime = 6n + 1; u = 1, . . ., p - 1 |
| [3] P62 |
2a+b, |
(1/3)(x + y), (1/3)(-x + 2y), z; |
3a; 6c |
3b; 6c |
3 × 6c |
[3] P64 |
2a + b, |
(1/3)(x + y), (1/3)(-x + 2y), z; |
|
-a + b, c |
±((1/3), (2/3), 0) |
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-a+b, c |
±((1/3), (2/3), 0) |
| [7] P62 |
3a + b, |
(1/7)(2x + y), (1/7)(-x + 3y), z; |
3a; 3 × 6c |
3b; 3 × 6c |
7 × 6c |
[7] P64 |
3a + b, |
(1/7)(2x + y), (1/7)(-x + 3y), z; |
|
-a + 2b, c |
±((1/7), (3/7), 0); ±((3/7), (2/7), 0); |
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-a + 2b, c |
±((1/7), (3/7), 0); ±((3/7), (2/7), 0); |
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±((5/7), (1/7), 0) |
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±((5/7), (1/7), 0) |
| [7] P62 |
3a+2b, |
(1/7)(x + 2y), (1/7)(-2x + 3y), z; |
3a; 3 × 6c |
3b; 3 × 6c |
7 × 6c |
[7] P64 |
3a+2b, |
(1/7)(x + 2y), (1/7)(-2x + 3y), z; |
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-2a+b, c |
±((2/7), (3/7), 0); ±((3/7), (1/7), 0); |
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-2a+b, c |
±((2/7), (3/7), 0); ±((3/7), (1/7), 0); |
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±((1/7), (5/7), 0) |
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±((1/7), (5/7), 0) |
| [p] P62 |
qa + rb, |
(1/p)((q - r)x + ry), |
3a; ((p - 1)/2) × |
3b; ((p - 1)/2) × |
p × 6c |
[p] P64 |
qa + rb, |
(1/p)((q - r)x + ry), |
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-ra +(q - r)b, c |
(1/p)( - rx + qy), z; +((ur/p), (uq/p), 0) |
6c |
6c |
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-ra +(q - r)b, c |
(1/p)( - rx + qy), z; +((ur/p), (uq/p), 0) |
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p = prime = q2 - qr + r2 = 6n + 1; |
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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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q, r = 1, 2, . . .; q> r; u = 1, . . ., p - 1 |
| [4] P62 |
2a, 2b, c |
(1/2)x, (1/2)y, z; +((1/2), 0, 0); |
3a; 3 × 3b |
2 × 6c |
4 × 6c |
[4] P64 |
2a, 2b, c |
(1/2)x, (1/2)y, z; +((1/2), 0, 0); |
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+(0, (1/2), 0); +((1/2), (1/2), 0) |
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+(0, (1/2), 0); +((1/2), (1/2), 0) |
| [p2] P62 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
3a; ((p2 - 1)/2) × |
3b; ((p2 - 1)/2) × |
p2 × 6c |
[p2] P64 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
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p = prime = 6n - 1; u, v = 1, . . ., p - 1 |
6c |
6c |
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p = prime = 6n - 1; u, v = 1, . . ., p - 1 |
