I4/mcm | No. 140 | I4/m2/c2/m | D4h18 |
Axes | Coordinates | Wyckoff positions | ||||||||||||
4a | 4b | 4c | 4d | 8e | 8f | 8g | 8h | 16i | 16j | 16k | 16l | |||
32m | ||||||||||||||
I Maximal translationengleiche subgroups | ||||||||||||||
[2] I-42m | x + (1/2), y, z + (1/4) | 4c | 2a; 2b | 4d | 4e | 8i | 8h | 2 × 4e | 8i | 16j | 8f; 8g | 16j | 2 × 8i | |
(121) | 2 × 16j | |||||||||||||
[2] I-4c2 | 4a | 4c | 4b | 4d | 8e | 8f | 8g | 8h | 2 × 8e | 16i | 16i | 16i | ||
(120) | 2 × 16i | |||||||||||||
[2] I4cm | 4a | 4b | 4a | 4b | 8c | 2 × 4a | 2 × 4b | 8c | 16d | 16d | 16d | 2 × 8c | ||
(108) | 2 × 16d | |||||||||||||
[2] I422 | x, y, z + (1/4) | 2a; 2b | 4c | 4e | 4d | 8g | 2 × 4e | 8f | 8j | 2 × 8g | 8h; 8i | 16k | 16k | |
(97) | 2 × 16k | |||||||||||||
[2] I4/m | 4e | 4d | 2a; 2b | 4c | 8f | 2 × 4e | 8g | 8h | 16i | 16i | 2 × 8h | 16i | ||
(87) | 2 × 16i | |||||||||||||
[2] Ibam | 4a | 4b | 4c | 4d | 8e | 8h | 8i | 8j | 16k | 8f; 8g | 2 × 8j | 16k | ||
(72) | 2 × 16k | |||||||||||||
[2] Fmmm | a - b, | (1/2)(x - y) + (1/4), | 8f | 8i | 8e | 4a; 4b | 8c; 8d | 16j | 2 × 8i | 8g; 8h | 16k; 16l | 32p | 2 × 16o | 16m; 16n |
(69) | a + b, c | (1/2)(x + y) + (1/4), z | 2 × 32p | |||||||||||
II Maximal klassengleiche subgroups | ||||||||||||||
Loss of centring translations | ||||||||||||||
[2] P42/ncm | origin 1: x, y, z | 4a | 4e | 4b | 4e | 4c; 4d | 8f | 2 × 4e | 8i | 8g; 8h | 16j | 16j | 2 × 8i | |
(138) | origin 2: x + (1/4), y - (1/4), z + (1/4) | 2 × 16j | ||||||||||||
[2] P42/mbc | x + (1/2), y, z | 4d | 4b | 4c | 4a | 8g | 8f | 8e | 8h | 2 × 8g | 16i | 2 × 8h | 16i | |
(135) | 2 × 16i | |||||||||||||
[2] P42/nbc | origin 1: x, y, z | 4b | 4a | 4d | 4c | 8e | 8g | 8f | 8j | 16k | 8h; 8i | 16k | 16k | |
(133) | origin 2: x + (1/4), y - (1/4), z + (1/4) | 2 × 16k | ||||||||||||
[2] P42/mcm | x + (1/2), y, z | 4e | 2b; 2d | 4f | 2a; 2c | 8o | 8k | 4g; 4h | 4i; 4j | 16p | 8l; 8m | 2 × 8n | 2 × 8o | |
(132) | 2 × 16p | |||||||||||||
[2] P4/ncc | origin 1: x + (1/2), y, z + (1/4) | 4c | 4b | 4c | 4a | 8d | 2 × 4c | 8e | 8f | 16g | 16g | 16g | 16g | |
(130) | origin 2: x + (1/4), y + (1/4), z + (1/4) | 2 × 16g | ||||||||||||
[2] P4/mbm | 4e | 4f | 2a; 2b | 2c; 2d | 8k | 2 × 4e | 2 × 4f | 4g; 4h | 16l | 16l | 8i; 8j | 2 × 8k | ||
(127) | 2 × 16l | |||||||||||||
[2] P4/nbm | origin 1: x, y, z + (1/4) | 2a; 2b | 2c; 2d | 4g | 4h | 4e; 4f | 2 × 4g | 2 × 4h | 8m | 8i; 8j | 8k; 8l | 16n | 2 × 8m | |
(125) | origin 2: x + (1/4), y + (1/4), z + (1/4) | 2 × 16n | ||||||||||||
[2] P4/mcc | 2a; 2c | 4f | 2b; 2d | 4e | 8j | 4g; 4h | 8i | 8m | 2 × 8j | 8k; 8l | 2 × 8m | 16n | ||
(124) | 2 × 16n |
Axes | Coordinates | Wyckoff positions | ||||||
4a | 4b | 4c | 4d | 8e | 8f | |||
8g | 8h | 16i | 16j | |||||
16k | 16l | 32m | ||||||
Enlarged unit cell, isomorphic | ||||||||
[3] I4/mcm | a, b, 3c | x, y, (1/3)z; | 4a; 8f | 4b; 8g | 4c; 8f | 4d; 8g | 8e; 16l | 3 × 8f |
±(0, 0, (1/3)) | 3 × 8g | 8h; 16l | 16i; 32m | 16j; 32m | ||||
16k; 32m | 3 × 16l | 3 × 32m | ||||||
[p] I4/mcm | a, b, pc | 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) × 16l | p × 8f |
+(0, 0, (u/p)) | p × 8g | 8h; ((p - 1)/2) × 16l | 16i; ((p - 1)/2) × 32m | 16j; ((p - 1)/2) × 32m | ||||
p = prime > 2; | 16k; ((p - 1)/2) × 32m | p × 16l | p × 32m | |||||
u = 1, . . ., p - 1 | ||||||||
[9] I4/mcm | 3a, 3b, c | (1/3)x, (1/3)y, z; | 4a; 16i; 16j | 4b; 16j; 16l | 4c; 2 × 16k | 4d; 2 × 8h; 16k | 8e; 16i; 16l; 32m | 8f; 2 × 32m |
±((1/3), 0, 0); | 8g; 2 × 16l; 32m | 3 × 8h; 3 × 16k | 3 × 16i; 3 × 32m | 3 × 16j; 3 × 32m | ||||
±(0, (1/3), 0); | 9 × 16k | 3 × 16l; 3 × 32m | 9 × 32m | |||||
±((1/3), (1/3), 0); | ||||||||
±((1/3), (2/3), 0) | ||||||||
[p2] I4/mcm | pa, pb, c | (1/p)x, (1/p)y, z; | 4a; ((p - 1)/2) × 16i; | 4b; ((p - 1)/2) × 16j; | 4c; ((p2 - 1)/4) × 16k | 4d; (p - 1) × 8h; | 8e; ((p - 1)/2) × 16i; | 8f; ((p2 - 1)/4) × 32m |
+((u/p), (v/p), 0) | ((p - 1)/2) × 16j; | ((p - 1)/2) × 16l; | (((p - 1)2)/4) × 16k | ((p - 1)/2) × 16l; | ||||
p = prime > 2; | (((p - 1)(p - 3))/8) × 32m | (((p - 1)(p - 3))/8) × 32m | (((p - 1)2)/4) × 32m | |||||
u, v = 1, . . ., p - 1 | ||||||||
8g; (p - 1) × 16l; | p × 8h; | p × 16i; | p × 16j; | |||||
(((p - 1)2)/4) × 32m | ((p(p - 1))/2) × 16k | ((p(p - 1))/2) × 32m | ((p(p - 1))/2) × 32m | |||||
p2 × 16k | p × 16l; | p2 × 32m | ||||||
((p(p - 1))/2) × 32m |