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Axes |
Coordinates |
Wyckoff positions |
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8a |
8b |
16c |
24d |
48e |
| I Maximal translationengleiche subgroups |
| [2] I213 (199) |
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8a |
8a |
2 × 8a |
2 × 12b |
2 × 24c |
| [4] R-3 (148) |
(1/2)(-a + b + c), |
y + z, x + z, x + y |
1a; 3e |
1b; 3d |
2c; 6f |
2 × 6f |
4 × 6f |
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(1/2)(a - b + c), |
(rhombohedral |
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(1/2)(a + b - c) |
axes) |
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-a + b, -b + c, |
(1/3)(-2x + y + z), (1/3)(-x - y + 2z), |
3a; 9e |
3b; 9d |
6c; 18f |
2 × 18f |
4 × 18f |
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(1/2)(a + b + c) |
(2/3)(x + y + z) |
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(hexagonal axes) |
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| conjugate: |
a + b, -b - c, |
(1/3)(2x + y - z), (1/3)(x - y - 2z) + (1/2), |
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(1/2)(-a + b - c) |
(2/3)(-x + y - z) |
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(hexagonal axes) |
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| conjugate: |
-a - b, b - c, |
(1/3)(-2x - y - z) + (1/2), (1/3)(-x + y - 2z), |
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(1/2)(-a - b - c) |
(2/3)(x - y - z) |
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(hexagonal axes) |
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| conjugate: |
a - b, b + c, |
(1/3)(2x - y + z) - (1/2), (1/3)(x + y + 2z) - (1/2), |
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(1/2)(-a - b + c) |
(2/3)(-x - y + z) |
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(hexagonal axes) |
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| [3] Ibca (73) |
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8a |
8b |
16f |
8c; 8d; 8e |
3 × 16f |
| II Maximal klassengleiche subgroups |
| Loss of centring translations |
| [2] Pa-3 (205) |
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4a; 4b |
8c |
2 × 8c |
24d |
2 × 24d |
| [2] Pa-3 (205) |
-b, a, c |
-y + (1/4), x - (1/4), z + (1/4) |
8c |
4a; 4b |
2 × 8c |
24d |
2 × 24d |
| Enlarged unit cell, isomorphic |
| [27]Ia-3 |
3a, 3b, 3c |
(1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); ±(0, (1/3), 0); |
8a; 16c; |
8b; 16c; |
3 × 16c; |
3 × 24d; |
27 × 48e |
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±(0, 0, (1/3)); ±(0, (1/3), (1/3)); ±((1/3), 0, (1/3)); |
4 × 48e |
4 × 48e |
8 × 48e |
12 × 48e |
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±((1/3), (1/3), 0); ±(0, (1/3), (2/3)); ±((1/3), 0, (2/3)); |
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±((1/3), (2/3), 0); ±((1/3), (1/3), (1/3)); ±((1/3), (1/3), (2/3)); |
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±((1/3), (2/3), (1/3)); ±((2/3), (1/3), (1/3)) |
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| [p3] Ia-3 |
pa, pb, pc |
(1/p)x, (1/p)y, (1/p)z; +((u/p), (v/p), (w/p)) |
8a; ((p - 1)/2) × 16c; |
8b; ((p - 1)/2) × 16c; |
p × 16c; |
p × 24d; |
p3 × 48e |
|
p = prime > 2; |
((p(p2 - 1))/6) × 48e |
((p(p2 - 1))/6) × 48e |
((p(p2 - 1))/3) × 48e |
((p(p2 - 1))/2) × 48e |
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u, v, w = 1, . . ., p - 1 |
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