|
Axes |
Coordinates |
Wyckoff positions |
|
|
|
2a |
6b |
8c |
12d |
12e |
16f |
|
|
|
|
|
|
|
24g |
48h |
| I Maximal translationengleiche subgroups |
| [2] I23 |
|
|
2a |
6b |
8c |
12d |
12e |
2 × 8c |
| (197) |
|
|
|
|
|
|
24f |
2 × 24f |
| [4] R-3 |
(1/2)(-a + b + c), |
y + z, x + z, x + y |
1a |
3e |
1b; 3d |
6f |
6f |
2c; 6f |
| (148) |
(1/2)(a - b + c), |
(rhombohedral |
|
|
|
|
2 × 6f |
4 × 6f |
|
(1/2)(a + b - c) |
axes) |
|
|
|
|
|
|
|
-a + b, -b + c, |
(1/3)(-2x + y + z), |
3a |
9e |
3b; 9d |
18f |
18f |
6c; 18f |
|
(1/2)(a + b + c) |
(1/3)(-x - y + 2z), (2/3)(x + y + z) |
|
|
|
|
2 × 18f |
4 × 18f |
|
(hexagonal axes) |
|
|
|
|
|
|
| conjugate: |
a + b, -b - c, |
(1/3)(2x + y - z), (1/3)(x - y - 2z), |
|
|
|
|
|
|
|
(1/2)(-a + b - c) |
(2/3)(-x + y - z) |
|
|
|
|
|
|
|
(hexagonal axes) |
|
|
|
|
|
|
| conjugate: |
-a - b, b - c, |
(1/3)(-2x - y - z), (1/3)(-x + y - 2z), |
|
|
|
|
|
|
|
(1/2)(a - b - c) |
(2/3)(x - y - z) |
|
|
|
|
|
|
|
(hexagonal axes) |
|
|
|
|
|
|
| conjugate: |
a - b, b + c, |
(1/3)(2x - y + z), (1/3)(x + y + 2z), |
|
|
|
|
|
|
|
(1/2)(-a - b + c) |
(2/3)(-x - y + z) |
|
|
|
|
|
|
|
(hexagonal axes) |
|
|
|
|
|
|
| [3] Immm |
|
|
2a |
2b; 2c; 2d |
8k |
4e; 4g; 4i |
4f; 4h; 4j |
16o |
| (71) |
|
|
|
|
|
|
8l; 8m; 8n |
3 × 16o |
| II Maximal klassengleiche subgroups |
| Loss of centring translations |
| [2] Pn-3 |
origin 1 : |
x, y, z |
2a |
6d |
4b; 4c |
12f |
12g |
2 × 8e |
| (201) |
origin 2 : |
x + (1/4), y + (1/4), z + (1/4) |
|
|
|
|
24h |
2 × 24h |
| [2] Pm-3 |
|
|
1a; 1b |
3c; 3d |
8i |
6e; 6h |
6f; 6g |
2 × 8i |
| (200) |
|
|
|
|
|
|
12j; 12k |
2 × 24l |
| Enlarged unit cell, isomorphic |
| [27] Im-3 |
3a, 3b, 3c |
(1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); |
2a; 12d; 16f; |
6b; 12d; |
8c; 16f; |
3 × 12d; |
3 × 12e; |
3 × 16f; |
|
|
±(0, (1/3), 0); ±(0, 0, (1/3)); |
24g |
2 × 12e; |
4 × 48h |
6 × 24g; |
6 × 24g; 3 × 48h |
8 × 48h |
|
|
±(0, (1/3), (1/3)); ±((1/3), 0, (1/3)); |
|
3 × 24g; 48h |
|
3 × 48h |
|
|
|
|
±((1/3), (1/3), 0); ±(0, (1/3), (2/3)); |
|
|
|
|
9 × 24g; 9 × 48h |
27 × 48h |
|
|
±((1/3), 0, (2/3)); ±((1/3), (2/3), 0); |
|
|
|
|
|
|
|
|
±((1/3), (1/3), (1/3)); ±((2/3), (1/3), (1/3)); |
|
|
|
|
|
|
|
|
±((1/3), (2/3), (1/3)); ±((1/3), (1/3), (2/3)) |
|
|
|
|
|
|
| [p3] Im-3 |
pa, pb, pc |
(1/p)x, (1/p)y, (1/p)z; |
2a; |
6b; |
8c; |
p × 12d; |
p × 12e; |
p × 16f; |
|
|
+((u/p), (v/p), (w/p)) |
((p - 1)/2) × 12d; |
((p - 1)/2) × 12d; |
((p - 1)/2) × 16f; |
p(p - 1) × 24g; |
p(p - 1) × 24g; |
((p(p2 - 1))/3) × |
|
p = prime > 2; u, v, w = 1, . . ., p - 1 |
((p - 1)/2) × 16f; |
(p - 1) × 12e; |
((p(p2 - 1))/6) × 48h |
((p(p - 1)2)/4) × 48h |
((p(p - 1)2)/4) × 48h |
48h |
|
|
|
(((p - 1)2)/4) × 24g; |
((3(p - 1)2)/4) × 24g; |
|
|
|
|
|
|
|
(((p2 - 1)(p - 3))/24) × |
(((p - 1)3)/8) × 48h |
|
|
|
|
|
|
|
48h |
|
|
|
|
|
|
|
|
|
|
|
|
p2 × 24g; |
p3 × 48h |
|
|
|
|
|
|
|
((p2(p - 1))/2) × 48h |
|
