P42/mmc No. 131 P42/m2/m2/c D4h9


Axes Coordinates Wyckoff positions
2a 2b 2c 2d 2e 2f 4g 4h 4i 4j 4k
4l 4m 8n 8o 8p 8q 16r
I Maximal translationengleiche subgroups
[2] P-4m2 (115) x, y, z + (1/4) 2e 2f 2g 2g 1a; 1d 1b; 1c 2 × 2e 2 × 2f 2 × 2g 4j 4k
4j 4k 4h; 4i 2 × 4j 2 × 4k 8l 2 × 8l
[2] P-42c (112) x, y, z + (1/4) 2a 2c 2d 2b 2e 2f 4k 4l 4m 4g 4h
4j 4i 8n 8n 8n 8n 2 × 8n
[2] P42mc (105) 2a 2b 2c 2c 2a 2b 2 × 2a 2 × 2b 2 × 2c 4d 4e
4d 4e 8f 2 × 4d 2 × 4e 8f 2 × 8f
[2] P4222 (93) 2a 2b 2c 2d 2e 2f 4g 4h 4i 4j 4k
4l 4m 4n; 4o 8p 8p 8p 2 × 8p
[2] P42/m (84) 2a 2b 2c 2d 2e 2f 4g 4h 4i 4j 4j
4j 4j 8k 8k 8k 2 × 4j 2 × 8k
[2] Pmmm (47) 1a; 1c 1f; 1h 1d; 1e 1b; 1g 2q 2t 2 × 2q 2 × 2t 2r; 2s 2i; 2n 2l; 2o
2j; 2m 2k; 2p 8[alpha] 4u; 4w 4v; 4x 4y; 4z 2 × 8[alpha]
[2] Cccm (66) a - b, a + b, c (1/2)(x - y), (1/2)(x + y), z 4c 4d 4f 4e 4a 4b 8i 8j 8k 8l 8l
8l 8l 8g; 8h 16m 16m 2 × 8l 2 × 16m
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] P42/ncm a - b, a + b, c origin 1 : (1/2)(x - y), 4a 4e 4d 4c 4b 4e 8f 2 × 4e 8i 8g 8i
(138) (1/2)(x + y), z + (1/4); +((1/2), (1/2), 0) 8h 8i 16j 16j 2 × 8i 16j 2 × 16j
origin 2 : (1/2)(x - y) - (1/4),
(1/2)(x + y) + (1/4), z; +((1/2), (1/2), 0)
[2] P42/ncm a - b, a + b, c origin 1 : (1/2)(x - y) + (1/2), 4e 4a 4c 4d 4e 4b 2 × 4e 8f 8i 8i 8h
(138) (1/2)(x + y), z + (1/4); +((1/2), (1/2), 0) 8i 8g 16j 2 × 8i 16j 16j 2 × 16j
origin 2 : (1/2)(x - y) + (1/4),
(1/2)(x + y) + (1/4), z; +((1/2), (1/2), 0)
[2] P42/mnm a - b, a + b, c (1/2)(x - y), (1/2)(x + y), z; 2a; 2b 4c 4g 4f 4e 4d 2 × 4e 8h 8j 2 × 4f 8i
(136) +((1/2), (1/2), 0) 2 × 4g 8i 16k 2 × 8j 16k 2 × 8i 2 × 16k
[2] P42/mnm a - b, a + b, c (1/2)(x - y) + (1/2), (1/2)(x + y), z; 4c 2a; 2b 4f 4g 4d 4e 8h 2 × 4e 8j 8i 2 × 4g
(136) +((1/2), (1/2), 0) 8i 2 × 4f 16k 16k 2 × 8j 2 × 8i 2 × 16k
[2] P42/nnm a - b, a + b, c origin 1 : (1/2)(x - y), 4g 4d 4f 4e 2a; 2b 4c 2 × 4g 8h 8m 8m 8l
(134) (1/2)(x + y), z + (1/4); +((1/2), (1/2), 0) 8m 8k 8i; 8j 2 × 8m 16n 16n 2 × 16n
origin 2 : (1/2)(x - y) - (1/4),
(1/2)(x + y) + (1/4), z; +((1/2), (1/2), 0)
[2] P42/nnm a - b, a + b, c origin 1 : (1/2)(x - y) + (1/2), 4d 4g 4e 4f 4c 2a; 2b 8h 2 × 4g 8m 8k 8m
(134) (1/2)(x + y), z + (1/4); +((1/2), (1/2), 0) 8l 8m 8i; 8j 16n 2 × 8m 16n 2 × 16n
origin 2 : (1/2)(x - y) + (1/4),
(1/2)(x + y) + (1/4), z; +((1/2), (1/2), 0)
[2] P42/mcm a - b, a + b, c (1/2)(x - y), (1/2)(x + y), z; 2a; 2c 4f 4j 4i 2b; 2d 4e 4g; 4h 8k 8o 2 × 4i 8n
(132) +((1/2), (1/2), 0) 2 × 4j 8n 8l; 8m 2 × 8o 16p 2 × 8n 2 × 16p
[2] P42/mcm a - b, a + b, c (1/2)(x - y) + (1/2), (1/2)(x + y), z; 4f 2a; 2c 4i 4j 4e 2b; 2d 8k 4g; 4h 8o 8n 2 × 4j
(132) +((1/2), (1/2), 0) 8n 2 × 4i 8l; 8m 16p 2 × 8o 2 × 8n 2 × 16p


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









































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