| P61 |
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P65 |
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Axes |
Coordinates |
Wyckoff positions |
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Axes |
Coordinates |
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6a |
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| I Maximal translationengleiche subgroups |
| [2] P31 (144) |
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2 × 3a |
[2] P32 (145) |
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| [3] P1121 (4) |
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3 × 2a |
[3] P1121 (4) |
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| II Maximal klassengleiche subgroups |
| Enlarged unit cell, isomorphic |
| [5] P65 |
a, b, 5c |
x, y, (1/5) z; ±(0, 0, (1/5)); ±(0, 0, (2/5)) |
5 × 6a |
[5] P61 |
a, b, 5c |
x, y, (1/5) z; ±(0, 0, (1/5)); ±(0, 0, (2/5)) |
| (170) |
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(169) |
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| [p] P65 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
p × 6a |
[p] P61 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
| (170) |
p = prime = 6n - 1; u = 1, . . ., p - 1 |
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(169) |
p = prime = 6n - 1; u = 1, . . ., p - 1 |
| [7] P61 |
a, b, 7c |
x, y, (1/7) z; ±(0, 0, (1/7)); |
7 × 6a |
[7] P65 |
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] P61 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
p × 6a |
[p] P65 |
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] P61 |
2a + b, -a + b, c |
(1/3)(x + y), (1/3)(-x + 2y), z; ±((1/3), (2/3), 0) |
3 × 6a |
[3] P65 |
2a + b, -a + b, c |
(1/3)(x + y), (1/3)(-x + 2y), z; ±((1/3), (2/3), 0) |
| [7] P61 |
3a + b, |
(1/7)(2x + y), (1/7)(-x + 3y), z; |
7 × 6a |
[7] P65 |
3a + b, |
(1/7)(2x + y), (1/7)(-x + 3y), z; |
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-a + 2b, c |
±((1/7), (3/7), 0); ±((3/7), (2/7), 0); ±((5/7), (1/7), 0) |
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-a + 2b, c |
±((1/7), (3/7), 0); ±((3/7), (2/7), 0); ±((5/7), (1/7), 0) |
| [7] P61 |
3a + 2b, |
(1/7)(x + 2y), (1/7)(-2x + 3y), z; |
7 × 6a |
[7] P65 |
3a + 2b, |
(1/7)(x + 2y), (1/7)(-2x + 3y), z; |
|
-2a + b, c |
±((2/7), (3/7), 0); ±((3/7), (1/7), 0); ±((1/7), (5/7), 0) |
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-2a + b, c |
±((2/7), (3/7), 0); ±((3/7), (1/7), 0); ±((1/7), (5/7), 0) |
| [p] P61 |
qa + rb, |
(1/p)((q - r)x + ry), (1/p)(-rx + qy), z; |
p × 6a |
[p] P65 |
qa + rb, |
(1/p)((q - r)x + ry), (1/p)(-rx + qy), z; |
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-ra +(q - r)b, c |
+((ur/p), (uq/p), 0) |
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-ra +(q - r)b, c |
+((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] P61 |
2a, 2b, c |
(1/2)x, (1/2)y, z; +((1/2), 0, 0); |
4 × 6a |
[4] P65 |
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] P61 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
p2 × 6a |
[p2] P65 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
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p = prime = 3n - 1; u, v = 1, . . ., p - 1 |
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p = prime = 3n - 1; u, v = 1, . . ., p - 1 |
