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Axes |
Coordinates |
Wyckoff positions |
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1a |
1b |
3c |
3d |
4e |
6f |
6g |
12h |
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12i |
24j |
| I Maximal translationengleiche subgroups |
| [2] P23 |
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1a |
1b |
3c |
3d |
4e |
6f |
6i |
6g; 6h |
| (195) |
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12j |
2 × 12j |
| [4] R3m |
(rhombohedral axes) |
1a |
1a |
3b |
3b |
1a; 3b |
2 × 3b |
2 × 3b |
2 × 6c |
| (160) |
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2 × 3b; 6c |
4 × 6c |
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a - b, b - c, |
(1/3)(2x - y - z), (1/3)(x + y - 2z), |
3a |
3a |
9b |
9b |
3a; 9b |
2 × 9b |
2 × 9b |
2 × 18c |
|
a + b + c |
(1/3)(x + y + z) |
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2 × 9b; 18c |
4 × 18c |
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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-42m |
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1a |
1b |
1d; 2f |
1c; 2e |
4n |
2g; 4i |
2h; 4j |
4k; 4l; 4m |
| (111) |
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4n; 8o |
3 × 8o |
| 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 |
| Enlarged unit cell, non-isomorphic |
| [2] F-43c |
2a, 2b, 2c |
(1/2)x, (1/2)y, (1/2)z; +((1/2), 0, 0) |
8a |
8b |
24c |
24d |
32e |
48f |
48g |
96h |
| (219) |
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96h |
2 × 96h |
| [2] F-43m |
2a, 2b, 2c |
(1/2)x, (1/2)y, (1/2)z; +((1/2), 0, 0) |
4a; 4b |
4c; 4d |
24g |
24f |
2 × 16e |
2 × 24f |
2 × 24g |
96i |
| (216) |
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2 × 48h |
2 × 96i |
| [4] I-43m |
2a, 2b, 2c |
(1/2)x, (1/2)y, (1/2)z; +((1/2), 0, 0); |
2a; 6b |
8c |
24g |
12d; 12e |
8c; 24g |
2 × 12e; 24f |
2 × 24g |
2 × 48h |
| (217) |
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+(0, (1/2), 0); +(0, 0, (1/2)) |
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2 × 24g; 48h |
4 × 48h |
| [4] I-43m |
2a, 2b, 2c |
(1/2)x + (1/4), (1/2)y + (1/4), (1/2)z + (1/4); |
8c |
2a; 6b |
12d; 12e |
24g |
8c; 24g |
2 × 24g |
2 × 12e; 24f |
2 × 48h |
| (217) |
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+((1/2), 0, 0); +(0, (1/2), 0); |
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2 × 24g; 48h |
4 × 48h |
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+(0, 0, (1/2)) |
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Axes |
Coordinates |
Wyckoff positions |
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1a |
1b |
3c |
3d |
4e |
6f |
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6g |
12h |
12i |
24j |
| Enlarged unit cell, isomorphic |
| [27] P-43m |
3a, 3b, 3c |
(1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); |
1a; 2 × 4e; 6f; |
1b; 2 × 4e; 6g; |
3c; 6g; 12h; |
3d; 6f; 12h; |
3 × 4e; |
3 × 6f; 6 × 12i; |
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±(0, (1/3), 0); ±(0, 0, (1/3)); |
12i |
12i |
3 × 12i; 24j |
3 × 12i; 24j |
6 × 12i; 24j |
3 × 24j |
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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 × 6g; 6 × 12i; |
3 × 12h; |
9 × 12i; |
27 × 24j |
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±((1/3), 0, (2/3)); ±((1/3), (2/3), 0); |
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3 × 24j |
12 × 24j |
9 × 24j |
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±((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] P-43m |
pa, pb, pc |
(1/p)x, (1/p)y, (1/p)z; |
1a; (p - 1) × 4e; |
1b; (p - 1) × 4e; |
3c; ((p - 1)/2) × 6g; |
3d; ((p - 1)/2) × 6f; |
p × 4e; |
p × 6f; |
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+((u/p), (v/p), (w/p)) |
((p - 1)/2) × 6f; |
((p - 1)/2) × 6g; |
((p - 1)/2) × 12h; |
((p - 1)/2) × 12h; |
p(p - 1) × 12i; |
p(p - 1) × 12i; |
|
p = prime > 2; |
(((p - 1)(p - 2))/2) × 12i; |
(((p - 1)(p - 2))/2) × 12i; |
((p(p - 1))/2) × 12i; |
((p(p - 1))/2) × 12i; |
((p(p - 1)(p - 2))/6) × |
((p(p - 1)2)/4) × 24j |
|
u, v, w = 1, . . ., p - 1 |
(((p - 1)(p - 2)(p - 3))/24) |
(((p - 1)(p - 2)(p - 3))/24) |
(((p2 - 1)(p - 2))/8) × |
(((p2 - 1)(p - 2))/8) × |
24j |
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× 24j |
× 24j |
24j |
24j |
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p × 6g; |
p × 12h; |
p2 × 12i; |
p3 × 24j |
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p(p - 1) × 12i; |
((p(p2 - 1))/2) × 24j |
((p2(p - 1))/2) × 24j |
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((p(p - 1)2)/4) × 24j |
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