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Axes |
Coordinates |
Wyckoff positions |
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2a |
2b |
2c |
2d |
4e |
4f |
8g |
| I Maximal translationengleiche subgroups |
| [2] I112 (5) |
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2a |
2a |
2b |
2b |
2 × 2a |
2 × 2b |
2 × 4c |
| II Maximal klassengleiche subgroups |
| Loss of centring translations |
| [2] P-4 (81) |
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1a; 1d |
1b; 1c |
2g |
2g |
2e; 2f |
2 × 2g |
2 × 4h |
| [2] P-4 (81) |
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x + (1/2), y, z + (1/4) |
2g |
2g |
1a; 1d |
1b; 1c |
2 × 2g |
2e; 2f |
2 × 4h |
| Enlarged unit cell, isomorphic |
| [3] I-4 |
a, b, 3c |
x, y, (1/3)z; +(0, 0, (1/3)) |
2a; 4e |
2b; 4e |
2d; 4f |
2c; 4f |
3 × 4e |
3 × 4f |
3 × 8g |
| [p] I-4 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
2a; |
2b; |
2c(d*); |
2d(c*); |
p × 4e |
p × 4f |
p × 8g |
|
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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| [5] I-4 |
a + 2b, -2a + b, c |
(1/5)(x + 2y), (1/5)(-2x + y), z; |
2a; 8g |
2b; 8g |
2c; 8g |
2d; 8g |
4e; 2 × 8g |
4f; 2 × 8g |
5 × 8g |
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±((1/5), (3/5), 0); ±((2/5), (1/5), 0) |
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| [5] I-4 |
a - 2b, 2a + b, c |
(1/5)(x - 2y), (1/5)(2x + y), z; |
2a; 8g |
2b; 8g |
2c; 8g |
2d; 8g |
4e; 2 × 8g |
4f; 2 × 8g |
5 × 8g |
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±((1/5), (2/5), 0); ±((3/5), (1/5), 0) |
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| [p] I-4 |
qa - rb, |
(1/p)(qx - ry), (1/p)(rx + qy), z; |
2a; |
2b; |
2c; |
2d; |
4e; |
4f; |
p × 8g |
|
ra + qb, c |
+((uq/p), (ur/p), 0) |
((p - 1)/4) × 8g |
((p - 1)/4) × 8g |
((p - 1)/4) × 8g |
((p - 1)/4) × 8g |
((p - 1)/2) × 8g |
((p - 1)/2) × 8g |
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p = q2 + r2 = prime = 4n + 1; |
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q = 2n + 1 ≥ 1; r = ± 2n'≠ 0; |
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u = 1, . . ., p - 1 |
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| [9] I-4 |
3a, 3b, c |
(1/3)x, (1/3)y, z; |
2a; 2 × 8g |
2b; 2 × 8g |
2c; 2 × 8g |
2d; 2 × 8g |
4e; 4 × 8g |
4f; 4 × 8g |
9 × 8g |
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±((1/3), 0, 0); ±(0, (1/3), 0); |
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±((1/3), (1/3), 0); ±((1/3), (2/3), 0) |
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| [p2] I-4 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
2a; |
2b; |
2c; |
2d; |
4e; |
4f; |
p2 × 8g |
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p = prime = 4n - 1; u, v = 1, . . ., p - 1 |
((p2 - 1)/4) × 8g |
((p2 - 1)/4) × 8g |
((p2 - 1)/4) × 8g |
((p2 - 1)/4) × 8g |
((p2 - 1)/2) × 8g |
((p2 - 1)/2) × 8g |
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| * p = 4n - 1 |
