|
Axes |
Coordinates |
Wyckoff positions |
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2a |
6b |
6c |
6d |
8e |
12f |
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12g |
12h |
24i |
| I Maximal translationengleiche subgroups |
| [2] P23 |
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1a; 1b |
3c; 3d |
6h |
6g |
2 × 4e |
6f; 6i |
| (195) |
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2 × 6h |
2 × 6g |
2 × 12j |
| [4] R3c |
(rhombohedral axes) |
2a |
6b |
6b |
6b |
2a; 6b |
2 × 6b |
| (161) |
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2 × 6b |
2 × 6b |
4 × 6b |
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a - b, b - c, |
(1/3)(2x - y - z), (1/3)(x + y - 2z), |
6a |
18b |
18b |
18b |
6a; 18b |
2 × 18b |
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a + b + c |
(1/3)(x + y + z) |
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2 × 18b |
2 × 18b |
4 × 18b |
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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), |
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-a + b - c |
(1/3)(-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), |
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a - b - c |
(1/3)(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), |
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-a - b + c |
(1/3)(-x - y + z) |
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(hexagonal axes) |
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| [3] P-42c |
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x + (1/2), y, z + (1/4) |
2b |
2a; 2c; 2d |
2e; 4i |
2f; 4j |
8n |
4g; 4h; 4m |
| (112) |
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2 × 4i; 4k |
2 × 4j; 4l |
3 × 8n |
| conjugate: |
b, c, a |
y + (1/2), z, x + (1/4) |
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| conjugate: |
c, a, b |
z + (1/2), x, y + (1/4) |
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| II Maximal klassengleiche subgroups |
| Enlarged unit cell, non-isomorphic |
| [4] I-43d |
2a, 2b, 2c |
(1/2)x, (1/2)y, (1/2)z; +((1/2), 0, 0); |
16c |
2 × 24d |
48e |
12a; 12b; 24d |
16c; 48e |
2 × 48e |
| (220) |
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+(0, (1/2), 0); +(0, 0, (1/2)) |
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2 × 48e |
4 × 24d |
4 × 48e |
| [4] I-43d |
2a, 2b, 2c |
(1/2)x + (1/4), (1/2)y + (1/4), (1/2)z + (1/4); |
16c |
2 × 24d |
12a; 12b; 24d |
48e |
16c; 48e |
2 × 48e |
| (220) |
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+((1/2), 0, 0); +(0, (1/2), 0); |
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4 × 24d |
2 × 48e |
4 × 48e |
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+(0, 0, (1/2)) |
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| Enlarged unit cell, isomorphic |
| [27] P-43n |
3a, 3b, 3c |
(1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); |
2a; 2 × 8e; |
6b; 12f; 12g; |
6c; 12g; |
6d; 12h; |
3 × 8e; |
3 × 12f; |
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±(0, (1/3), 0); ±(0, 0, (1/3)); |
12f; 24i |
12h; 5 × 24i |
6 × 24i |
6 × 24i |
8 × 24i |
12 × 24i |
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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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3 × 12g; |
3 × 12h; |
27 × 24i |
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±((1/3), 0, (2/3)); ±((1/3), (2/3), 0); |
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12 × 24i |
12 × 24i |
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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] P-43n |
pa, pb, pc |
(1/p)x, (1/p)y, (1/p)z; +((u/p), (v/p), (w/p)) |
2a; |
6b; ((p - 1)/2) × 12f; |
6c; |
6d; |
p × 8e; |
p × 12f; |
|
p = prime > 4; u, v, w = 1, . . ., p - 1 |
(p - 1) × 8e; |
((p - 1)/2) × 12g; |
((p - 1)/2) × 12g; |
((p - 1)/2) × 12h; |
((p(p2 - 1))/3) × 24i |
((p(p2 - 1))/2) × 24i |
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((p - 1)/2) × 12f; |
((p - 1)/2) × 12h; |
((p(p2 - 1))/4) × 24i |
((p(p2 - 1))/4) × 24i |
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((p3 - 7p + 6)/12) × |
(((p - 1)2(p + 2))/4) × |
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24i |
24i |
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p × 12g; |
p × 12h; |
p3 × 24i |
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((p(p2 - 1))/2) × 24i |
((p(p2 - 1))/2) × 24i |
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