P42/mcm No. 132 P42/m2/c2/m D4h10


Axes Coordinates Wyckoff positions
2a 2b 2c 2d 4e 4f 4g 4h 4i 4j
8k 8l 8m 8n 8o 16p
I Maximal translationengleiche subgroups
[2] P-4c2 (116) x, y, z + (1/4) 2a 2c 2b 2d 4i 4i 4g 4h 4e 4f
2 × 4i 8j 8j 8j 8j 2 × 8j
[2] P-42m (111) x, y, z + (1/4) 2g 1a; 1c 2h 1b; 1d 2e; 2f 4m 2 × 2g 2 × 2h 4n 4n
2 × 4m 4i; 4k 4j; 4l 8o 2 × 4n 2 × 8o
[2] P42cm (101) 2a 2a 2b 2b 4c 4c 2 × 2a 2 × 2b 4d 4d
2 × 4c 8e 8e 8e 2 × 4d 2 × 8e
[2] P4222 (93) x, y, z + (1/4) 2e 2a 2f 2b 2c; 2d 4i 4g 4h 4n 4o
2 × 4i 4j; 4l 4k; 4m 8p 8p 2 × 8p
[2] P42/m (84) 2a 2e 2b 2f 4i 2c; 2d 4g 4h 4j 4j
2 × 4i 8k 8k 2 × 4j 8k 2 × 8k
[2] Pccm (49) 2a 2e 2b 2h 2f; 2g 2c; 2d 4m 4n 4q 4q
4o; 4p 4i; 4k 4j; 4l 2 × 4q 8r 2 × 8r
[2] Cmmm (65) a - b, a + b, c (1/2)(x - y), (1/2)(x + y), z 2a; 2d 4k 2b; 2c 4l 8m 4e; 4f 2 × 4k 2 × 4l 4h; 4i 4g; 4j
2 × 8m 16r 16r 8p; 8q 8n; 8o 2 × 16r
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] P42/nmc a - b, a + b, c origin 1 : (1/2)(x - y), 4c 2a; 2b 4d 4d 8f 8e 2 × 4c 2 × 4d 8g 8g
(137) (1/2)(x + y), z + (1/4); +((1/2), (1/2), 0) 16h 2 × 8f 16h 16h 2 × 8g 2 × 16h
origin 2 : (1/2)(x - y) - (1/4),
(1/2)(x + y) + (1/4), z; +((1/2), (1/2), 0)
[2] P42/nmc a - b, a + b, c origin 1 : (1/2)(x - y) + (1/2), 4d 4d 4c 2a; 2b 8f 8e 2 × 4d 2 × 4c 8g 8g
(137) (1/2)(x + y), z + (1/4); +((1/2), (1/2), 0) 16h 16h 2 × 8f 16h 2 × 8g 2 × 16h
origin 2 : (1/2)(x - y) + (1/4),
(1/2)(x + y) + (1/4), z; +((1/2), (1/2), 0)
[2] P42/mbc a - b, a + b, c (1/2)(x - y), (1/2)(x + y), z; 4a 4b 4c 4d 8g 8h 8e 8f 8h 8h
(135) +((1/2), (1/2), 0) 16i 16i 2 × 8g 2 × 8h 16i 2 × 16i
[2] P42/mbc a - b, a + b, c (1/2)(x - y) + (1/2), (1/2)(x + y), z; 4c 4d 4a 4b 8g 8h 8f 8e 8h 8h
(135) +((1/2), (1/2), 0) 16i 2 × 8g 16i 2 × 8h 16i 2 × 16i
[2] P42/nbc a - b, a + b, c origin 1 : (1/2)(x - y), 4b 4d 4a 4c 8j 8e 8g 8f 8i 8h
(133) (1/2)(x + y), z + (1/4); +((1/2), (1/2), 0) 16k 16k 2 × 8j 16k 16k 2 × 16k
origin 2 : (1/2)(x - y) - (1/4),
(1/2)(x + y) + (1/4), z; +((1/2), (1/2), 0)
[2] P42/nbc a - b, a + b, c origin 1 : (1/2)(x - y) + (1/2), 4a 4c 4b 4d 8j 8e 8f 8g 8i 8h
(133) (1/2)(x + y), z + (1/4); +((1/2), (1/2), 0) 16k 2 × 8j 16k 16k 16k 2 × 16k
origin 2 : (1/2)(x - y) + (1/4),
(1/2)(x + y) + (1/4), z; +((1/2), (1/2), 0)
[2] P42/mmc a - b, a + b, c (1/2)(x - y), (1/2)(x + y), z; 2a; 2b 2e; 2f 2c; 2d 4i 8n 8q 4g; 4h 2 × 4i 4k; 4l 4j; 4m
(131) +((1/2), (1/2), 0) 16r 2 × 8n 16r 2 × 8q 8o; 8p 2 × 16r
[2] P42/mmc a - b, a + b, c (1/2)(x - y) + (1/2), (1/2)(x + y), z; 2c; 2d 4i 2a; 2b 2e; 2f 8n 8q 2 × 4i 4g; 4h 4k; 4l 4j; 4m
(131) +((1/2), (1/2), 0) 16r 16r 2 × 8n 2 × 8q 8o; 8p 2 × 16r


Axes Coordinates Wyckoff positions
  2a 2b 2c 2d 4e 4f
4g 4h 4i 4j 8k 8l
8m 8n 8o 16p
   Enlarged unit cell, isomorphic
[3] P42/mcm a, b, 3c x, y, (1/3)z; 2a; 4g 2b; 4g 2c; 4h 2d; 4h 4e; 8k 4f; 8k
±(0, 0, (1/3)) 3 × 4g 3 × 4h 4i; 8o 4j; 8o 3 × 8k 8l; 16p
8m; 16p 8n; 16p 3 × 8o 3 × 16p
[p] P42/mcm a, b, pc x, y, (1/p)z; 2a; ((p - 1)/2) × 4g 2b; ((p - 1)/2) × 4g 2c; ((p - 1)/2) × 4h 2d; ((p - 1)/2) × 4h 4e; ((p - 1)/2) × 8k 4f; ((p - 1)/2) × 8k
+(0, 0, (u/p)) p × 4g p × 4h 4i; ((p - 1)/2) × 8o 4j; ((p - 1)/2) × 8o p × 8k 8l; ((p - 1)/2) × 16p
p = prime > 2; 8m; ((p - 1)/2) × 16p 8n; ((p - 1)/2) × 16p p × 8o p × 16p
u = 1, . . ., p - 1
[9] P42/mcm 3a, 3b, c (1/3)x, (1/3)y, z; 2a; 4i; 4j; 8n 2b; 8l; 8o 2c; 4i; 4j; 8n 2d; 8m; 8o 4e; 8l; 8m; 16p 4f; 4 × 8n
±((1/3), 0, 0); 4g; 2 × 8o; 16p 4h; 2 × 8o; 16p 3 × 4i; 3 × 8n 3 × 4j; 3 × 8n 8k; 4 × 16p 3 × 8l; 3 × 16p
±(0, (1/3), 0); 3 × 8m; 3 × 16p 9 × 8n 3 × 8o; 3 × 16p 9 × 16p
±((1/3), (1/3), 0);
±((1/3), (2/3), 0)
[p2] P42/mcm pa, pb, c (1/p)x, (1/p)y, z; 2a; ((p - 1)/2) × 4i; 2b; ((p - 1)/2) × 8l; 2c; ((p - 1)/2) × 4i; 2d; ((p - 1)/2) × 8m; 4e; ((p - 1)/2) × 8l; 4f; ((p2 - 1)/2) × 8n
+((u/p), (v/p), 0) ((p - 1)/2) × 4j; ((p - 1)/2) × 8o; ((p - 1)/2) × 4j; ((p - 1)/2) × 8o; ((p - 1)/2) × 8m;
p = prime > 2; (((p - 1)2)/4) × 8n (((p - 1)(p - 3))/8) × 16p (((p - 1)2)/4) × 8n (((p - 1)(p - 3))/8) × 16p (((p - 1)2)/4) × 16p
u, v = 1, . . ., p - 1 4g; (p - 1) × 8o; 4h; (p - 1) × 8o; p × 4i; p × 4j; 8k; ((p2 - 1)/2) × 16p p × 8l;
(((p - 1)2)/4) × 16p (((p - 1)2)/4) × 16p ((p(p - 1))/2) × 8n ((p(p - 1))/2) × 8n ((p(p - 1))/2) × 16p
p × 8m; p2 × 8n p × 8o; p2 × 16p
((p(p - 1))/2) × 16p ((p(p - 1))/2) × 16p









































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