|
Axes |
Coordinates |
Wyckoff positions |
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8a |
12b |
24c |
| I Maximal translationengleiche subgroups |
| [4] R3 (146) |
(1/2)(-a + b + c), (1/2)(a - b + c), |
y + z, x + z, x + y |
1a; 3b |
2 × 3b |
4 × 3b |
|
(1/2)(a + b - c) |
(rhombohedral axes) |
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-a + b, -b + c, (1/2)(a + b + c) |
(1/3)(-2x + y + z), (1/3)(-x - y + 2z), |
3a; 9b |
2 × 9b |
4 × 9b |
|
(hexagonal axes) |
(2/3)(x + y + z) |
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|
| conjugate: |
a + b, -b - c, (1/2)(-a + b - c) |
(1/3)(2x + y - z), (1/3)(x - y - 2z) + (1/2), |
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|
(hexagonal axes) |
(2/3)(-x + y - z) |
|
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|
| conjugate: |
-a - b, b - c, (1/2)(a - b - c) |
(1/3)(-2x - y - z) + (1/2), (1/3)(-x + y - 2z), |
|
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|
(hexagonal axes) |
(2/3)(x - y - z) |
|
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|
| conjugate: |
a - b, b + c, (1/2)(-a - b + c) |
(1/3)(2x - y + z) - (1/2), (1/3)(x + y + 2z) - (1/2), |
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|
(hexagonal axes) |
(2/3)(-x - y + z) |
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| [3] I212121 (24) |
|
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8d |
4a; 4b; 4c |
3 × 8d |
| II Maximal klassengleiche subgroups |
| Loss of centring translations |
| [2] P213 (198) |
|
|
2 × 4a |
12b |
2 × 12b |
| Enlarged unit cell, isomorphic |
| [27] I213 |
3a, 3b, 3c |
(1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); ±(0, (1/3), 0); |
3 × 8a; 8 × 24c |
3 × 12b; 12 × 24c |
27 × 24c |
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±(0, 0, (1/3)); ±(0, (1/3), (1/3)); ±((1/3), 0, (1/3)); |
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±((1/3), (1/3), 0); ±(0, (1/3), (2/3)); ±((1/3), 0, (2/3)); ±((1/3), (2/3), 0); |
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±((1/3), (1/3), (1/3)); ±((1/3), (1/3), (2/3)); ±((1/3), (2/3), (1/3)); ±((2/3), (1/3), (1/3)) |
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| [p3] I213 |
pa, pb, pc |
(1/p)x, (1/p)y, (1/p)z; +((u/p), (v/p), (w/p)) |
p × 8a; ((p(p2 - 1))/3) × 24c |
p × 12b; ((p(p2 - 1))/2) × 24c |
p3 × 24c |
|
p = prime > 2; |
u, v, w = 1, . . ., p - 1 |
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