|
Axes |
Coordinates |
Wyckoff positions |
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1a |
1b |
1c |
3d |
| I Maximal translationengleiche subgroups |
| [3] P1 (1) |
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1a |
1a |
1a |
3 × 1a |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, non-isomorphic |
| [3] P32(145) |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
3a |
3a |
3a |
3 × 3a |
| [3] P31(144) |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
3a |
3a |
3a |
3 × 3a |
| [3] R3 (146) |
a - b, a + 2b, 3c |
(1/3)(2x - y), (1/3)(x + y), (1/3)z; ±(0, 0, (1/3)) |
3 × 3a |
9b |
9b |
3 × 9b |
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(hexagonal axes) |
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| [3] R3 (146) |
a - b, a + 2b, 3c |
(1/3)(2x - y), (1/3)(x + y) - (1/3), (1/3)z; ±(0, 0, (1/3)) |
9b |
3 × 3a |
9b |
3 × 9b |
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(hexagonal axes) |
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| [3] R3 (146) |
a - b, a + 2b, 3c |
(1/3)(2x - y), (1/3)(x + y) + (1/3), (1/3)z; ±(0, 0, (1/3)) |
9b |
9b |
3 × 3a |
3 × 9b |
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(hexagonal axes) |
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| [3] R3 (146) |
2a + b, -a + b, 3c |
(1/3)(x + y), (1/3)(-x + 2y), (1/3)z; ±(0, 0, (1/3)) |
3 × 3a |
9b |
9b |
3 × 9b |
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(hexagonal axes) |
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| [3] R3 (146) |
2a + b, -a + b, 3c |
(1/3)(x + y) + (1/3), (1/3)(-x + 2y), (1/3)z; ±(0, 0, (1/3)) |
9b |
3 × 3a |
9b |
3 × 9b |
|
(hexagonal axes) |
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| [3] R3 (146) |
2a + b, -a + b, 3c |
(1/3)(x + y) - (1/3), (1/3)(-x + 2y), (1/3)z; ±(0, 0, (1/3)) |
9b |
9b |
3 × 3a |
3 × 9b |
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(hexagonal axes) |
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| Enlarged unit cell, isomorphic |
| [2] P3 |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
2 × 1a |
2 × 1b |
2 × 1c |
2 × 3d |
| [3] P3 |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
3 × 1a |
3 × 1b |
3 × 1c |
3 × 3d |
| [p] P3 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
p × 1a |
p × 1b |
p × 1c |
p × 1d |
|
p = prime; u = 1, . . ., p - 1 |
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| [3] P3 |
2a + b, -a + b, c |
(1/3)(x + y), (1/3)(-x + 2y), z; ±((1/3), (2/3), 0) |
1a; 1b; 1c |
3d |
3d |
3 × 3d |
| [3] P3 |
2a + b, -a + b, c |
(1/3)(x + y) + (1/3), (1/3)(-x + 2y), z; ±((1/3), (2/3), 0) |
3d |
1a; 1b; 1c |
3d |
3 × 3d |
| [3] P3 |
2a + b, -a + b, c |
(1/3)(x + y) - (1/3), (1/3)(-x + 2y), z; ±((1/3), (2/3), 0) |
3d |
3d |
1a; 1b; 1c |
3 × 3d |
| [7] P3 |
3a + b, -a + 2b, c |
(1/7)(2x + y), (1/7)(-x + 3y), z; ±((1/7), (3/7), 0); |
1a; 2 × 3d |
1b; 2 × 3d |
1c; 2 × 3d |
7 × 3d |
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±((3/7), (2/7), 0); ±((5/7), (1/7), 0) |
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| [7] P3 |
3a + 2b, -2a + b, c |
(1/7)(x + 2y), (1/7)(-2x + 3y), z; ±((2/7), (3/7), 0); |
1a; 2 × 3d |
1c; 2 × 3d |
1b; 2 × 3d |
7 × 3d |
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±((3/7), (1/7), 0); ±((1/7), (5/7), 0) |
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| [p] P3 |
qa + rb, |
(1/p)((q - r)x + ry), (1/p)(-rx + qy), z; |
1a; ((p - 1)/3) × 3d |
1b(c*); ((p - 1)/3) × 3d |
1c(b*); ((p - 1)/3) × 3d |
p × 3d |
|
-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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q, r = 1, 2, . . .; q> r; u = 1, . . ., p - 1 |
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| [4] P3 |
2a, 2b, c |
(1/2)x, (1/2)y, z; +((1/2), 0, 0); +(0, (1/2), 0); |
1a; 3d |
1c; 3d |
1b; 3d |
4 × 3d |
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+((1/2), (1/2), 0) |
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| [p2] P3 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
1a; ((p2 - 1)/3) × 3d |
1c; ((p2 - 1)/3) × 3d |
1b; ((p2 - 1)/3) × 3d |
p2 × 3d |
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p = prime = 3n - 1; u, v = 1, . . ., p - 1 |
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| * q + r = 3n - 1 |
