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









































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