I-42m No. 121 D2d11


Axes Coordinates Wyckoff positions
2a 2b 4c 4d 4e 8f
8g 8h 8i 16j
I Maximal translationengleiche subgroups
[2] I-4 (82) 2a 2b 4f 2c; 2d 4e 8g
8g 2 × 4f 8g 2 × 8g
[2] I222 (23) 2a 2c 2b; 2d 4j 4i 4e; 4g
4f; 4h 2 × 4j 8k 2 × 8k
[2] Fmm2 a - b, (1/2)(x - y), (1/2)(x + y), z 4a 4a 8b 8b 2 × 4a 16e
  (42) a + b, c 16e 2 × 8b 8c; 8d 2 × 16e
II Maximal klassengleiche subgroups
   Loss of centring translations
[2] P-421c 2a 2b 4d 4d 4c 8e
  (114) 8e 2 × 4d 8e 2 × 8e
[2] P-421m x + (1/2), y, z + (1/4) 2c 2c 4d 2a; 2b 2 × 2c 8f
  (113) 8f 2 × 4d 2 × 4e 2 × 8f
[2] P-42c x + (1/2), y, z + (1/4) 2b 2d 2a; 2c 2e; 2f 4m 4g; 4h
  (112) 4i; 4j 4k; 4l 8n 2 × 8n
[2] P-42m 1a; 1b 1c; 1d 2e; 2f 4m 2g; 2h 4i; 4j
  (111) 4k; 4l 2 × 4m 2 × 4n 2 × 8o
   Enlarged unit cell, isomorphic
[3] I-42m a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 2a; 4e 2b; 4e 4c; 8h 4d; 8h 3 × 4e 8f; 16j
8g; 16j 3 × 8h 3 × 8i 3 × 16j
[p] I-42m a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 2a; ((p - 1)/2) × 4e 2b; ((p - 1)/2) × 4e 4c; ((p - 1)/2) × 8h 4d; ((p - 1)/2) × 8h p × 4e 8f; ((p - 1)/2) × 16j
p = prime > 2; 8g; ((p - 1)/2) × 16j p × 8h p × 8i p × 16j
u = 1, . . ., p - 1
[9] I-42m 3a, 3b, c (1/3)x, (1/3)y, z; 2a; 8f; 8i 2b; 8g; 8i 4c; 8f; 8g; 16j 4d; 2 × 16j 4e; 2 × 8i; 16j 3 × 8f; 3 × 16j
±((1/3), 0, 0); ±(0, (1/3), 0); 3 × 8g; 3 × 16j 8h; 4 × 16j 3 × 8i; 3 × 16j 9 × 16j
±((1/3), (1/3), 0); ±((1/3), (2/3), 0)
[p2] I-42m pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) 2a; ((p - 1)/2) × 8f; 2b; ((p - 1)/2) × 8g; 4c; ((p - 1)/2) × 8f; 4d; ((p2 - 1)/4) × 16j 4e; (p - 1) × 8i; p × 8f;
p = prime > 2; ((p - 1)/2) × 8i; ((p - 1)/2) × 8i; ((p - 1)/2) × 8g; (((p - 1)2)/4) × 16j ((p(p - 1))/2) × 16j
u, v = 1, . . ., p - 1 (((p - 1)(p - 3))/8) × 16j (((p - 1)(p - 3))/8) × 16j (((p - 1)2)/4) × 16j
p × 8g; 8h; ((p2 - 1)/2) × 16j p × 8i; p2 × 16j
((p(p - 1))/2) × 16j ((p(p - 1))/2) × 16j









































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