I4/mmm No. 139 I4/m2/m2/m D4h17


Axes Coordinates Wyckoff positions
2a 2b 4c 4d 4e 8f 8g 8h 8i 8j 16k 16l
16m 16n 32o
I Maximal translationengleiche subgroups
[2] I-42m 2a 2b 4c 4d 4e 8i 8h 8i 8f 8g 16j 16j
  (121) 2 × 8i 16j 2 × 16j
[2] I-4m2 2a 2b 4f 2c; 2d 4e 8h 2 × 4f 8g 8i 8i 2 × 8h 16j
  (119) 16j 2 × 8i 2 × 16j
[2] I4mm 2a 2a 4b 4b 2 × 2a 8c 2 × 4b 8c 8d 8d 16e 16e
  (107) 2 × 8c 2 × 8d 2 × 16e
[2] I422 2a 2b 4c 4d 4e 8j 8f 8g 8h 8i 2 × 8j 16k
  (97) 16k 16k 2 × 16k
[2] I4/m 2a 2b 4c 4d 4e 8f 8g 8h 8h 8h 16i 2 × 8h
  (87) 16i 16i 2 × 16i
[2] Immm 2a 2c 2b; 2d 4j 4i 8k 2 × 4j 8n 4e; 4g 4f; 4h 16o 2 × 8n
  (71) 16o 8l; 8m 2 × 16o
[2] Fmmm a - b, (1/2)(x - y), 4a 4b 8e 8f 8i 8c; 8d 16j 8g; 8h 16o 16o 16k; 16l 2 × 16o
  (69) a + b, c (1/2)(x + y), z 16m; 16n 32p 2 × 32p
II Maximal klassengleiche subgroups
   Loss of centring translations
[2] P42/nmc origin 1: x, y, z 2a 2b 4d 4d 4c 8e 2 × 4d 8f 8g 8g 16h 16h
  (137) origin 2: x + (1/4), y - (1/4), z + (1/4) 16h 2 × 8g 2 × 16h
[2] P42/mnm 2a 2b 4c 4d 4e 8j 8h 4f; 4g 8i 8i 16k 2 × 8i
  (136) 2 × 8j 16k 2 × 16k
[2] P42/nnm origin 1: x, y, z 2a 2b 4c 4d 4g 4e; 4f 8h 8m 8i 8j 8k; 8l 16n
  (134) origin 2: x + (1/4), y - (1/4), z + (1/4) 2 × 8m 16n 2 × 16n
[2] P42/mmc x + (1/2), y, z 2d 2c 2a; 2b 2e; 2f 4i 8n 4g; 4h 8q 4j; 4k 4l; 4m 2 × 8n 2 × 8q
  (131) 16r 8o; 8p 2 × 16r
[2] P4/nmm origin 1: x, y + (1/2), z + (1/4) 2c 2c 4f 2a; 2b 2 × 2c 4d; 4e 2 × 4f 8j 8i 8i 8g; 8h 16k
  (129) origin 2: x + (1/4), y + (1/4), z + (1/4) 2 × 8j 2 × 8i 2 × 16k
[2] P4/mnc 2a 2b 4c 4d 4e 8g 8f 8h 8h 8h 2 × 8g 2 × 8h
  (128) 16i 16i 2 × 16i
[2] P4/nnc origin 1: x, y, z 2a 2b 4c 4d 4e 8f 8g 8h 8i 8j 16k 16k
  (126) origin 2: x + (1/4), y + (1/4), z + (1/4) 16k 16k 2 × 16k
[2] P4/mmm 1a; 1d 1b; 1c 2e; 2f 4i 2g; 2h 8r 2 × 4i 4j; 4k 4l; 4o 4m; 4n 16u 8p; 8q
  (123) 2 × 8r 8s; 8t 2 × 16u


Axes Coordinates Wyckoff positions
  2a 2b 4c 4d 4e 8f
8g 8h 8i 8j 16k
16l 16m 16n 32o
   Enlarged unit cell, isomorphic
[3] I4/mmm a, b, 3c x, y, (1/3)z; 2a; 4e 2b; 4e 4c; 8g 4d; 8g 3 × 4e 8f; 16m
±(0, 0, (1/3)) 3 × 8g 8h; 16m 8i; 16n 8j; 16n 16k; 32o
16l; 32o 3 × 16m 3 × 16n 3 × 32o
[p] I4/mmm a, b, pc x, y, (1/p)z; 2a; ((p - 1)/2) × 4e 2b; ((p - 1)/2) × 4e 4c; ((p - 1)/2) × 8g 4d; ((p - 1)/2) × 8g p × 4e 8f; ((p - 1)/2) × 16m
+(0, 0, (u/p)) p × 8g 8h; ((p - 1)/2) × 16m 8i; ((p - 1)/2) × 16n 8j; ((p - 1)/2) × 16n 16k; ((p - 1)/2) × 32o
p = prime > 2; 16l; ((p - 1)/2) × 32o p × 16m p × 16n p × 32o
u = 1, . . ., p - 1
[9] I4/mmm 3a, 3b, c (1/3)x, (1/3)y, z; 2a; 8h; 8i 2b; 8h; 8j 4c; 8i; 8j; 16l 4d; 16k; 16n 4e; 16m; 16n 8f; 16k; 16m; 32o
±((1/3), 0, 0); 8g; 2 × 16n; 32o 3 × 8h; 3 × 16l 3 × 8i; 3 × 16l 3 × 8j; 3 × 16l 3 × 16k; 3 × 32o
±(0, (1/3), 0); 9 × 16l 3 × 16m; 3 × 32o 3 × 16n; 3 × 32o 9 × 32o
±((1/3), (1/3), 0);
±((1/3), (2/3), 0)
[p2] I4/mmm pa, pb, c (1/p)x, (1/p)y, z; 2a; ((p - 1)/2) × 8h; 2b; ((p - 1)/2) × 8h; 4c; ((p - 1)/2) × 8i; 4d; ((p - 1)/2) × 16k; 4e; ((p - 1)/2) × 16m; 8f; ((p - 1)/2) × 16k;
+((u/p), (v/p), 0) ((p - 1)/2) × 8i; ((p - 1)/2) × 8j; ((p - 1)/2) × 8j; ((p - 1)/2) × 16n; ((p - 1)/2) × 16n; ((p - 1)/2) × 16m;
p = prime > 2; (((p - 1)(p - 3))/8) × 16l (((p - 1)(p - 3))/8) × 16l (((p - 1)2)/4) × 16l (((p - 1)(p - 3))/8) × 32o (((p - 1)(p - 3))/8) × 32o (((p - 1)2)/4) × 32o
u, v = 1, . . ., p - 1 8g; (p - 1) × 16n; p × 8h; p × 8i; p × 8j; p × 16k;
(((p - 1)2)/4) × 32o ((p(p - 1))/2) × 16l ((p(p - 1))/2) × 16l ((p(p - 1))/2) × 16l ((p(p - 1))/2) × 32o
p2 × 16l p × 16m; p × 16n p2 × 32o
((p(p - 1))/2) × 32o ((p(p - 1))/2) × 32o









































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