|
Axes |
Coordinates |
Wyckoff positions |
|
|
origin 1 |
origin 2 |
4a |
4b |
4c |
4d |
8e |
8f |
|
|
|
|
|
8g |
8h |
8i |
8j |
16k |
| I Maximal translationengleiche subgroups |
| [2] P-4b2 |
|
|
x + (1/4), |
4f |
4e |
2c; 2d |
2a; 2b |
8i |
2 × 4f |
| (117) |
|
|
y - (1/4), z + (1/4) |
|
2 × 4e |
8i |
8i |
4g; 4h |
2 × 8i |
| [2] P-42c |
|
|
x + (1/4), |
2b; 2d |
2a; 2c |
4m |
2e; 2f |
8n |
2 × 4m |
| (112) |
|
|
y - (1/4), z + (1/4) |
|
4k; 4l |
4g; 4i |
4h; 4j |
8n |
2 × 8n |
| [2] P42bc |
|
x + (1/2), y, z |
x + (1/4), |
4a |
4b |
4a |
4b |
8c |
2 × 4a |
| (106) |
|
|
y + (1/4), z |
|
2 × 4b |
8c |
8c |
8c |
2 × 8c |
| [2] P4222 |
|
x + (1/2), y, z - (1/4) |
x + (1/4), |
2a; 2b |
2c; 2d |
2e; 2f |
4i |
8p |
4g; 4h |
| (93) |
|
|
y + (1/4), z |
|
2 × 4i |
4j; 4m |
4k; 4l |
4n; 4o |
2 × 8p |
| [2] P42/n |
|
|
x + (1/2), y, z |
4e |
4f |
4e |
2a; 2b |
4c; 4d |
2 × 4e |
| (86) |
|
|
|
|
2 × 4f |
8g |
8g |
8g |
2 × 8g |
| [2] Pban |
|
x + (1/2), y, z - (1/4) |
|
2a; 2d |
2b; 2c |
4k |
4l |
4e; 4f |
2 × 4k |
| (50) |
|
|
|
|
2 × 4l |
4g; 4j |
4h; 4i |
8m |
2 × 8m |
| [2] Ccce |
a - b, |
(1/2)(x - y) + (1/4), |
(1/2)(x - y), |
8g |
8h |
4a; 4b |
8h |
8c; 8d |
2 × 8g |
| (68) |
a + b, c |
(1/2)(x + y) + (1/4), z |
(1/2)(x + y), z |
|
2 × 8h |
16i |
16i |
8e; 8f |
2 × 16i |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, isomorphic |
| [3] P42/nbc |
a, b, 3c |
x, y, (1/3)z; |
x, y, (1/3)z; |
4a; 8f |
4b; 8g |
4c; 8f |
4d; 8g |
8e; 16k |
3 × 8f |
|
|
±(0, 0, (1/3)) |
±(0, 0, (1/3)) |
|
3 × 8g |
8h(i*); 16k |
8i(h*); 16k |
8j; 16k |
3 × 16k |
| [p] P42/nbc |
a, b, pc |
x, y, (1/p)z; |
x, y, (1/p)z; |
4a; ((p - 1)/2) × 8f |
4b; ((p - 1)/2) × 8g |
4c; ((p - 1)/2) × 8f |
4d; ((p - 1)/2) × 8g |
8e; ((p - 1)/2) × 16k |
p × 8f |
|
|
+(0, 0, (u/p)) |
+(0, 0, (u/p)) |
|
p × 8g |
8h(i† ); ((p - 1)/2) × 16k |
8i(h† ); ((p - 1)/2) × 16k |
8j; ((p - 1)/2) × 16k |
p × 16k |
|
p = prime > 2; u = 1, . . ., p - 1 |
|
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|
|
|
| [9] P42/nbc |
3a, 3b, c |
(1/3)x, (1/3)y, z; |
(1/3)x, (1/3)y, z; |
4a; 8h; 8i; 16k |
4b; 8h; 8i; 16k |
4c; 2 × 8j; 16k |
4d; 2 × 16k |
8e; 4 × 16k |
8f; 4 × 16k |
|
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±((1/3), 0, 0); ±(0, (1/3), 0); |
|
8g; 4 × 16k |
3 × 8h; 3 × 16k |
3 × 8i; 3 × 16k |
3 × 8j; 3 × 6k |
9 × 16k |
|
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±((1/3), (1/3), 0); ±((1/3), (2/3), 0) |
|
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|
| [p2] P42/nbc |
pa, pb, c |
(1/p)x, (1/p)y, z; |
(1/p)x, (1/p)y, z; |
4a; ((p - 1)/2) × 8h; |
4b; ((p - 1)/2) × 8h; |
4c; (p - 1) × 8j; |
4d; ((p2 - 1)/4) × 16k |
8e; ((p2 - 1)/2) × 16k |
8f; ((p2 - 1)/2) × |
|
|
+((u/p), (v/p), 0) |
+((u/p), (v/p), 0) |
((p - 1)/2) × 8i; |
((p - 1)/2) × 8i; |
(((p - 1)2)/4) × 16k |
|
|
16k |
|
p = prime > 2; |
(((p - 1)2)/4) × 16k |
(((p - 1)2)/4) × 16k |
|
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|
|
u, v = 1, . . ., p - 1 |
|
8g; ((p2 - 1)/2) × 16k |
p × 8h; |
p × 8i; |
p × 8j; |
p2 × 16k |
|
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|
|
((p(p - 1))/2) × 16k |
((p(p - 1))/2) × 16k |
((p(p - 1))/2) × 16k |
|
| * origin 1 |
| † origin 1 and p = 4n - 1 |
