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Axes |
Coordinates |
Wyckoff positions |
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1a |
1b |
1c |
1d |
2e |
2f |
2g |
4h |
| I Maximal translationengleiche subgroups |
| [2] P112(3) |
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1a |
1a |
1d |
1d |
2 × 1a |
2 × 1d |
1b; 1c |
2 × 2e |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, non-isomorphic |
| [2] I-4 |
a - b, |
(1/2)(x - y), (1/2)(x + y), (1/2)z; |
2a; 2b |
4e |
4f |
2c; 2d |
2 × 4e |
2 × 4f |
8g |
2 × 8g |
| (82) |
a + b, 2c |
+(0, 0, (1/2)) |
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| [2] I-4 |
a - b, |
(1/2)(x - y), (1/2)(x + y), (1/2)z + (1/4); |
4e |
2a; 2b |
2c; 2d |
4f |
2 × 4e |
2 × 4f |
8g |
2 × 8g |
| (82) |
a + b, 2c |
+(0, 0, (1/2)) |
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| Enlarged unit cell, isomorphic |
| [2] P-4 |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
1a; 1b |
2e |
1c; 1d |
2f |
2 × 2e |
2 × 2f |
2 × 2g |
2 × 4h |
| [2] P-4 |
a, b, 2c |
x, y, (1/2)z + (1/4); +(0, 0, (1/2)) |
2e |
1a; 1b |
2f |
1c; 1d |
2 × 2e |
2 × 2f |
2 × 2g |
2 × 4h |
| [3] P-4 |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
1a; 2e |
1b; 2e |
1c; 2f |
1d; 2f |
3 × 2e |
3 × 2f |
3 × 2g |
3 × 4h |
| [p] P-4 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
1a; ((p - 1)/2) × 2e |
1b; ((p - 1)/2) × 2e |
1c; ((p - 1)/2) × 2f |
1d; ((p - 1)/2) × 2f |
p × 2e |
p × 2f |
p × 2g |
p × 4h |
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p = prime > 2; u = 1, . . ., p - 1 |
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| [2] P-4 |
a - b, |
(1/2)(x - y), (1/2)(x + y), z; |
1a; 1c |
1b; 1d |
2g |
2g |
2e; 2f |
2 × 2g |
4h |
2 × 4h |
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a + b, c |
+((1/2), (1/2), 0) |
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| [2] P-4 |
a - b, |
(1/2)(x - y) + (1/2), (1/2)(x + y), z; |
2g |
2g |
1a; 1c |
1b; 1d |
2 × 2g |
2e; 2f |
4h |
2 × 4h |
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a + b, c |
+((1/2), (1/2), 0) |
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| [5] P-4 |
a + 2b, |
(1/5)(x + 2y), (1/5)(-2x + y), z; |
1a; 4h |
1b; 4h |
1c; 4h |
1d; 4h |
2e; 2 × 4h |
2f; 2 × 4h |
2g; 2 × 4h |
5 × 4h |
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-2a + b, c |
±((1/5), (3/5), 0); ±((2/5), (1/5), 0) |
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| [5] P-4 |
a - 2b, |
(1/5)(x - 2y), (1/5)(2x + y), z; |
1a; 4h |
1b; 4h |
1c; 4h |
1d; 4h |
2e; 2 × 4h |
2f; 2 × 4h |
2g; 2 × 4h |
5 × 4h |
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2a + b, c |
±((1/5), (2/5), 0); ±((3/5), (1/5), 0) |
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| [p] P-4 |
qa - rb, |
(1/p)(qx - ry), (1/p)(rx + qy), z; |
1a; ((p - 1)/4) × 4h |
1b; ((p - 1)/4) × 4h |
1c; ((p - 1)/4) × 4h |
1d; ((p - 1)/4) × 4h |
2e; |
2f; |
2g; |
p × 4h |
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ra + qb, c |
+((uq/p), (ur/p), 0) |
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((p - 1)/2) × 4h |
((p - 1)/2) × 4h |
((p - 1)/2) × 4h |
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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] P-4 |
3a, 3b, c |
(1/3)x, (1/3)y, z; |
1a; 2 × 4h |
1b; 2 × 4h |
1c; 2 × 4h |
1d; 2 × 4h |
2e; 4 × 4h |
2f; 4 × 4h |
2g; 4 × 4h |
9 × 4h |
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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] P-4 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
1a; ((p2 - 1)/4) × 4h |
1b; ((p2 - 1)/4) × 4h |
1c; ((p2 - 1)/4) × 4h |
1d; ((p2 - 1)/4) × 4h |
2e; |
2f; |
2g; |
p2 × 4h |
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p = prime = 4n - 1; |
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((p2 - 1)/2) × 4h |
((p2 - 1)/2) × 4h |
((p2 - 1)/2) × 4h |
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u, v = 1, . . ., p - 1 |
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