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Axes |
Coordinates |
Wyckoff positions |
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2a |
6b |
8c |
12d |
12e |
24f |
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24g |
48h |
| I Maximal translationengleiche subgroups |
| [2] I23 |
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2a |
6b |
8c |
12e |
12d |
2 × 12e |
| (197) |
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24f |
2 × 24f |
| [4] R3m |
(1/2)(-a + b + c), |
y + z, x + z, x + y |
1a |
3b |
1a; 3b |
6c |
2 × 3b |
2 × 6c |
| (160) |
(1/2)(a - b + c), |
(rhombohedral |
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2 × 3b; 6c |
4 × 6c |
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(1/2)(a + b - c) |
axes) |
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-a + b, -b + c, |
(1/3)(-2x + y + z), |
3a |
9b |
3a; 9b |
18c |
2 × 9b |
2 × 18c |
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(1/2)(a + b + c) |
(1/3)(-x - y + 2z), |
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2 × 9b; 18c |
4 × 18c |
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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), |
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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), |
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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), |
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(hexagonal axes) |
(2/3)(-x - y + z) |
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| [3] I-42m |
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2a |
2b; 4c |
8i |
4d; 8g |
4e; 8f |
2 × 8g; 8h |
| (121) |
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8i; 16j |
3 × 16j |
| conjugate: |
b, c, a |
y, z, x |
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| conjugate: |
c, a, b |
z, x, y |
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| II Maximal klassengleiche subgroups |
| Loss of centring translations |
| [2] P-43n |
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2a |
6b |
8e |
6c; 6d |
12f |
12g; 12h |
| (218) |
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24i |
2 × 24i |
| [2] P-43m |
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1a; 1b |
3c; 3d |
2 × 4e |
12h |
6f; 6g |
2 × 12h |
| (215) |
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2 × 12i |
2 × 24j |
| Enlarged unit cell, isomorphic |
| [27] I-43m |
3a, 3b, 3c |
(1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); |
2a; 2 × 8c; 12e; |
6b; 12e; 24f; |
3 × 8c; 6 × 24g; |
12d; 24f; |
3 × 12e; 6 × 24g; |
3 × 24f; |
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±(0, (1/3), 0); ±(0, 0, (1/3)); |
24g |
3 × 24g; 48h |
48h |
6 × 48h |
3 × 48h |
12 × 48h |
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±(0, (1/3), (1/3)); ±((1/3), 0, (1/3)); |
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±((1/3), (1/3), 0); ±(0, (1/3), (2/3)); |
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9 × 24g; 9 × 48h |
27 × 48h |
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±((1/3), 0, (2/3)); ±((1/3), (2/3), 0); |
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±((1/3), (1/3), (1/3)); ±((2/3), (1/3), (1/3)); |
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±((1/3), (2/3), (1/3)); ±((1/3), (1/3), (2/3)) |
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| [p3] I-43m |
pa, pb, pc |
(1/p)x, (1/p)y, (1/p)z; +((u/p), (v/p), (w/p)) |
2a; |
6b; |
p × 8c; |
12d; |
p × 12e; |
p × 24f; |
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p = prime > 2; u, v, w = 1, . . ., p - 1 |
(p - 1) × 8c; |
((p - 1)/2) × 12e; |
p(p - 1) × 24g; |
((p - 1)/2) × 24f; |
p(p - 1) × 24g; |
((p(p2 - 1))/2) × |
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((p - 1)/2) × 12e; |
((p - 1)/2) × 24f; |
((p(p - 1)(p - 2))/6) × |
((p(p2 - 1))/4) × 48h |
((p(p - 1)2)/4) × 48h |
48h |
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(((p - 1)(p - 2))/2) × 24g; |
((p(p - 1))/2) × 24g; |
48h |
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(((p - 1)(p - 2)(p - 3))/24) |
(((p2 - 1)(p - 2))/8) × |
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× 48h |
48h |
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p2 × 24g; |
p3 × 48h |
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((p2(p - 1))/2) × 48h |
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