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Axes |
Coordinates |
Wyckoff positions |
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16a |
16b |
24c |
24d |
32e |
48f |
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48g |
96h |
| I Maximal translationengleiche subgroups |
| [2] I-43d |
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16c |
16c |
24d |
12a; 12b |
2 × 16c |
2 × 24d |
| (220) |
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48e |
2 × 48e |
| [2] I4132 |
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16e |
8a; 8b |
12c; 12d |
24f |
2 × 16e |
2 × 24f |
| (214) |
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24g; 24h |
2 × 48i |
| [2] Ia-3 |
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8a; 8b |
16c |
24d |
24d |
2 × 16c |
2 × 24d |
| (206) |
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48e |
2 × 48e |
| [4] R-3c |
(1/2)(-a + b + c), |
y + z, x + z, x + y |
2b; 6d |
2a; 6e |
2 × 6e |
12f |
4c; 12f |
2 × 12f |
| (167) |
(1/2)(a - b + c), |
(rhombohedral |
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2 × 6e; 12f |
4 × 12f |
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(1/2)(a + b - c) |
axes) |
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-a + b, -b + c, |
(1/3)(-2x + y + z), |
6b; 18d |
6a; 18e |
2 × 18e |
36f |
12c; 36f |
2 × 36f |
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(1/2)(a + b + c) |
(1/3)(-x - y + 2z), |
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2 × 18e; 36f |
4 × 36f |
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(hexagonal axes) |
(2/3)(x + y + z) |
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| conjugate: |
a + b, -b - c, |
(1/3)(2x + y - z), |
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(1/2)(-a + b - c) |
(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, |
(1/3)(-2x - y - z) + (1/2), |
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(1/2)(a - b - c) |
(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, |
(1/3)(2x - y + z) - (1/2), |
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(1/2)(-a - b + c) |
(1/3)(x + y + 2z) - (1/2), |
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(hexagonal axes) |
(2/3)(-x - y + z) |
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| [3] I41/acd |
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origin 1: x, y - (1/4), z + (1/8) |
16c |
16f |
8b; 16e |
8a; 16e |
32g |
16d; 2 × 16e |
| (142) |
|
origin 2: x, y, z |
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16f; 32g |
3 × 32g |
| conjugate: |
b, c, a |
y, z, x (origin 2) |
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| conjugate: |
c, a, b |
z, x, y (origin 2) |
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| II Maximal klassengleiche subgroups |
| Enlarged unit cell, isomorphic |
| [27] Ia-3d |
3a, 3b, 3c |
(1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); |
16a; 32e; |
16b; 32e; |
24c; 48f; |
24d; 48f; |
3 × 32e; |
3 × 48f; |
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±(0, (1/3), 0); ±(0, 0, (1/3)); |
4 × 96h |
2 × 48g; |
2 × 48g; |
6 × 96h |
8 × 96h |
12 × 96h |
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±(0, (1/3), (1/3)); ±((1/3), 0, (1/3)); |
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3 × 96h |
5 × 96h |
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±((1/3), (1/3), 0); ±(0, (1/3), (2/3)); |
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±((1/3), 0, (2/3)); ±((1/3), (2/3), 0); |
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3 × 48g; |
27 × 96h |
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±((1/3), (1/3), (1/3)); ±((2/3), (1/3), (1/3)); |
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12 × 96h |
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±((1/3), (2/3), (1/3)); ±((1/3), (1/3), (2/3)) |
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| [p3] Ia-3d |
pa, pb, pc |
(1/p)x, (1/p)y, (1/p)z; +((u/p), (v/p), (w/p)) |
16a; |
16b; |
24c; ((p - 1)/2) × 48f; |
24d; |
p × 32e; |
p × 48f; |
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p = prime > 2; u, v, w = 1, . . ., p - 1 |
((p - 1)/2) × 32e; |
((p - 1)/2) × 32e; |
(p - 1) × 48g; |
((p - 1)/2) × 48f; |
((p(p2 - 1))/3) × 96h |
((p(p2 - 1))/2) × 96h |
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((p(p2 - 1))/6) × 96h |
(p - 1) × 48g; |
(((p - 1)2(p + 2))/4) × 96h |
((p(p2 - 1))/4) × 96h |
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((p3 - 4p + 3)/6) × 96h |
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p × 48g; |
p3 × 96h |
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((p(p2 - 1))/2) × 96h |
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