| P41 |
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P43 |
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Axes |
Coordinates |
Wyckoff positions |
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Axes |
Coordinates |
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4a |
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| I Maximal translationengleiche subgroups |
| [2] P1121 (4) |
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2 × 2a |
[2] P1121 (4) |
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| II Maximal klassengleiche subgroups |
| Enlarged unit cell, isomorphic |
| [3] P43 (78) |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
3 × 4a |
[3] P41 (76) |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
| [p] P43 (78) |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
p × 4a |
[p] P41 (76) |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
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p = prime = 4n - 1; u = 1, . . ., p - 1 |
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p = prime = 4n - 1; u = 1, . . ., p - 1 |
| [5] P41 |
a, b, 5c |
x, y, (1/5)z; ±(0, 0, (1/5)); ±(0, 0, (2/5)) |
5 × 4a |
[5] P43 |
a, b, 5c |
x, y, (1/5)z; ±(0, 0, (1/5)); ±(0, 0, (2/5)) |
| [p] P41 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
p × 4a |
[p] P43 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
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p = prime = 4n + 1; u = 1, . . ., p - 1 |
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p = prime = 4n + 1; u = 1, . . ., p - 1 |
| [2] P41 |
a - b, |
(1/2)(x - y), (1/2)(x + y), z; +((1/2), (1/2), 0) |
2 × 4a |
[2] P43 |
a - b, |
(1/2)(x - y), (1/2)(x + y), z; +((1/2), (1/2), 0) |
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a + b, c |
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a + b, c |
| [2] P41 |
a - b, |
(1/2)(x - y) + (1/2), (1/2)(x + y), z; +((1/2), (1/2), 0) |
2 × 4a |
[2] P43 |
a - b, |
(1/2)(x - y) + (1/2), (1/2)(x + y), z; +((1/2), (1/2), 0) |
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a + b, c |
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a + b, c |
| [5] P41 |
a + 2b, |
(1/5)(x + 2y), (1/5)(-2x + y), z; |
5 × 4a |
[5] P43 |
a + 2b, |
(1/5)(x + 2y), (1/5)(-2x + y), z; |
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-2a + b, c |
±((1/5), (3/5), 0); ±((2/5), (1/5), 0) |
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-2a + b, c |
±((1/5), (3/5), 0); ±((2/5), (1/5), 0) |
| [5] P41 |
a - 2b, |
(1/5)(x - 2y), (1/5)(2x + y), z; |
5 × 4a |
[5] P43 |
a - 2b, |
(1/5)(x - 2y), (1/5)(2x + y), z; |
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2a + b, c |
±((1/5), (2/5), 0); ±((3/5), (1/5), 0) |
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2a + b, c |
±((1/5), (2/5), 0); ±((3/5), (1/5), 0) |
| [p] P41 |
qa - rb, |
(1/p)(qx - ry), (1/p)(rx + qy), z; +((uq/p), (ur/p), 0) |
p × 4a |
[p] P43 |
qa - rb, |
(1/p)(qx - ry), (1/p)(rx + qy), z; +((uq/p), (ur/p), 0) |
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ra + qb, c |
q = 2n + 1 ≥ 1; r = ± 2n'≠ 0 |
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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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p = q2 + r2 = prime = 4n + 1; u = 1, . . ., p - 1 |
| [9] P41 |
3a, 3b, c |
(1/3)x, (1/3)y, z; ±((1/3), 0, 0); ±(0, (1/3), 0); |
9 × 4a |
[9] P43 |
3a, 3b, c |
(1/3)x, (1/3)y, z; ±((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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±((1/3), (1/3), 0); ±((1/3), (2/3), 0) |
| [p2] P41 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
p2 × 4a |
[p2] P43 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
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p = prime = 4n - 1; u, v = 1, . . ., p - 1 |
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p = prime = 4n - 1; u, v = 1, . . ., p - 1 |
