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Axes |
Coordinates |
Wyckoff positions |
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1a |
1b |
2c |
4d |
| I Maximal translationengleiche subgroups |
| [2] P112 (3) |
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1a |
1d |
1b; 1c |
2 × 2e |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, non-isomorphic |
| [2] I4 (79) |
a - b, a + b, 2c |
(1/2)(x - y), (1/2)(x + y), (1/2)z; +(0, 0, (1/2)) |
2 × 2a |
4b |
8c |
2 × 8c |
| [2] I4 (79) |
a - b, a + b, 2c |
(1/2)(x - y) + (1/2), (1/2)(x + y), (1/2)z; +(0, 0, (1/2)) |
4b |
2 × 2a |
8c |
2 × 8c |
| [2] P42 (77) |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
2a |
2b |
2 × 2c |
2 × 4d |
| Enlarged unit cell, isomorphic |
| [2] P4 |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
2 × 1a |
2 × 1b |
2 × 2c |
2 × 4d |
| [3] P4 |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
3 × 1a |
3 × 1b |
3 × 2c |
3 × 4d |
| [p] P4 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
p × 1a |
p × 1b |
p × 2c |
p × 4d |
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p = prime; u = 1, . . ., p - 1 |
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| [2] P4 |
a - b, a + b, c |
(1/2)(x - y), (1/2)(x + y), z; +((1/2), (1/2), 0) |
1a; 1b |
2c |
4d |
2 × 4d |
| [2] P4 |
a - b, a + b, c |
(1/2)(x - y) + (1/2), (1/2)(x + y), z; +((1/2), (1/2), 0) |
2c |
1a; 1b |
4d |
2 × 4d |
| [5] P4 |
a + 2b, -2a + b, c |
(1/5)(x + 2y), (1/5)(-2x + y), z; ±((2/5), (1/5), 0); ±((1/5), (3/5), 0) |
1a; 4d |
1b; 4d |
2c; 2 × 4d |
5 × 4d |
| [5] P4 |
a - 2b, 2a + b, c |
(1/5)(x - 2y), (1/5)(2x + y), z; ±((3/5), (1/5), 0); ±((1/5), (2/5), 0) |
1a; 4d |
1b; 4d |
2c; 2 × 4d |
5 × 4d |
| [p] P4 |
qa - rb, |
(1/p)(qx - ry), (1/p)(rx + qy), z; +((uq/p), (ur/p), 0) |
1a; ((p - 1)/4) × 4d |
1b; ((p - 1)/4) × 4d |
2c; ((p - 1)/2) × 4d |
p × 4d |
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ra + qb, c |
q = 2n + 1 ≥ 1; r = ± 2n'≠ 0; |
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p = q2 + r2 = prime = 4n + 1; u = 1, . . ., p - 1 |
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| [9] P4 |
3a, 3b, c |
(1/3)x, (1/3)y, z; ±((1/3), 0, 0); ±(0, (1/3), 0); |
1a; 2 × 4d |
1b; 2 × 4d |
2c; 4 × 4d |
9 × 4d |
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±((1/3), (1/3), 0); ±((1/3), (2/3), 0) |
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| [p2] P4 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
1a; ((p2 - 1)/4) × 4d |
1b; ((p2 - 1)/4) × 4d |
2c; ((p2 - 1)/2) × 4d |
p2 × 4d |
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p = prime = 4n - 1; u, v = 1, . . ., p - 1 |
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