P4222 No. 93 D45


Axes Coordinates Wyckoff positions
2a 2b 2c 2d 2e 2f 4g 4h 4i 4j 4k
4l 4m 4n 4o 8p
I Maximal translationengleiche subgroups
[2] P42 (77) 2a 2b 2c 2c 2a 2b 2 × 2a 2 × 2b 2 × 2c 4d 4d
4d 4d 4d 4d 2 × 4d
[2] P222 (16) 1a; 1d 1e; 1h 1c; 1f 1b; 1g 2q 2t 2 × 2q 2 × 2t 2r; 2s 2i; 2n 2l; 2o
2j; 2m 2k; 2p 4u 4u 2 × 4u
[2] C222 (21) a - b, a + b, c (1/2)(x - y), (1/2)(x + y), z + (1/4) 4i 4j 4k 4k 2a; 2d 2b; 2c 2 × 4i 2 × 4j 2 × 4k 8l 8l
8l 8l 4e; 4h 4f; 4g 2 × 8l
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] I4122 (98) a - b, a + b, 2c (1/2)(x - y) + (1/4), (1/2)(x + y) + (1/4), 8d 8e 8c 4a; 4b 8f 8f 16g 16g 2 × 8c 2 × 8d 2 × 8e
(1/2)z; +(0, 0, (1/2)) 16g 16g 16g 2 × 8f 2 × 16g
[2] I4122 (98) a - b, a + b, 2c (1/2)(x - y) - (1/4), (1/2)(x + y) + (1/4), 8e 8d 4a; 4b 8c 8f 8f 16g 16g 2 × 8c 16g 16g
(1/2)z; +(0, 0, (1/2)) 2 × 8e 2 × 8d 16g 2 × 8f 2 × 16g
[2] I4122 (98) a - b, a + b, 2c (1/2)(x - y) + (1/4), (1/2)(x + y) + (1/4), 8d 8e 4a; 4b 8c 8f 8f 16g 16g 2 × 8c 16g 16g
(1/2)z + (1/4); +(0, 0, (1/2)) 2 × 8d 2 × 8e 2 × 8f 16g 2 × 16g
[2] I4122 (98) a - b, a + b, 2c (1/2)(x - y) - (1/4), (1/2)(x + y) + (1/4), 8e 8d 8c 4a; 4b 8f 8f 16g 16g 2 × 8c 2 × 8e 2 × 8d
(1/2)z + (1/4); +(0, 0, (1/2)) 16g 16g 2 × 8f 16g 2 × 16g
[2] P4322 (95) a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 4a 4b 4a 4b 4c 4c 8d 8d 8d 8d 2 × 4b
2 × 4a 8d 2 × 4c 8d 2 × 8d
[2] P4322 (95) a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 4a 4b 4b 4a 4c 4c 8d 8d 8d 2 × 4a 8d
8d 2 × 4b 8d 2 × 4c 2 × 8d
[2] P42212 (94) a - b, a + b, c (1/2)(x - y), (1/2)(x + y), z; 2a; 2b 4d 4f 4e 4c 4d 2 × 4c 2 × 4d 8g 2 × 4e 8g
+((1/2), (1/2), 0) 2 × 4f 8g 8g 8g 2 × 8g
[2] P42212 (94) a - b, a + b, c (1/2)(x - y) + (1/2), (1/2)(x + y), z; 4d 2a; 2b 4e 4f 4d 4c 2 × 4d 2 × 4c 8g 8g 2 × 4f
+((1/2), (1/2), 0) 8g 2 × 4e 8g 8g 2 × 8g
[2] P4122 (91) a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 4a 4b 4a 4b 4c 4c 8d 8d 8d 8d 2 × 4b
2 × 4a 8d 8d 2 × 4c 2 × 8d
[2] P4122 (91) a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 4a 4b 4b 4a 4c 4c 8d 8d 8d 2 × 4a 8d
8d 2 × 4b 2 × 4c 8d 2 × 8d
   Enlarged unit cell, isomorphic
[3] P4222 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 2a; 4g 2b; 4h 2c; 4i 2d; 4i 2e; 4g 2f; 4h 3 × 4g 3 × 4h 3 × 4i 4j; 8p 4k; 8p
4l; 8p 4m; 8p 4o; 8p 4n; 8p 3 × 8p


Axes Coordinates Wyckoff positions
1a 1b 1c 1d 2e 2f
2g 2h 4i 4j 4k 4l
4m 4n 4o 8p
[p] P4222 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 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
p = prime > 2; p × 4g p × 4h p × 4i 4j; ((p - 1)/2) × 8p 4k; ((p - 1)/2) × 8p 4l; ((p - 1)/2) × 8p
u = 1, . . ., p - 1 4m; ((p - 1)/2) × 8p 4n(o*); 4o(n*); p × 8p
((p - 1)/2) × 8p ((p - 1)/2) × 8p
[2] P4222 a - b, (1/2)(x - y), (1/2)(x + y), 2e; 2f 4i 4o 4n 2a; 2b 2c; 2d
a + b, c z + (1/4); +((1/2), (1/2), 0) 4g; 4h 2 × 4i 8p 2 × 4n 8p 2 × 4o
8p 4j; 4m 4k; 4l 2 × 8p
[2] P4222 a - b, (1/2)(x - y) + (1/2), (1/2)(x + y), 4i 2e; 2f 4n 4o 2c; 2d 2a; 2b
a + b, c z + (1/4); +((1/2), (1/2), 0) 2 × 4i 4g; 4h 8p 8p 2 × 4o 8p
2 × 4n 4j; 4m 4k; 4l 2 × 8p
[9] P4222 3a, 3b, c (1/3)x, (1/3)y, z; ±((1/3), 0, 0); 2a; 4j; 4l; 8p 2b; 4k; 4m; 8p 2c; 4l; 4m; 8p 2d; 4j; 4k; 8p 2e; 4n; 4o; 8p 2f; 4n; 4o; 8p
±(0, (1/3), 0); ±((1/3), (1/3), 0); 4g; 4 × 8p 4h; 4 × 8p 4i; 4 × 8p 3 × 4j; 3 × 8p 3 × 4k; 3 × 8p 3 × 4l; 3 × 8p
±((1/3), (2/3), 0) 3 × 4m; 3 × 8p 3 × 4n; 3 × 8p 3 × 4o; 3 × 8p 9 × 8p
[p2] P4222 pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) 2a; ((p - 1)/2) × 4j; 2b; ((p - 1)/2) × 4k; 2c; ((p - 1)/2) × 4l; 2d; ((p - 1)/2) × 4j; 2e; ((p - 1)/2) × 4n; 2f; ((p - 1)/2) × 4n;
p = prime > 2; ((p - 1)/2) × 4l; ((p - 1)/2) × 4m; ((p - 1)/2) × 4m; ((p - 1)/2) × 4k; ((p - 1)/2) × 4o; ((p - 1)/2) × 4o;
u, v = 1, . . ., p - 1 (((p - 1)2)/4) × 8p (((p - 1)2)/4) × 8p (((p - 1)2)/4) × 8p (((p - 1)2)/4) × 8p (((p - 1)2)/4) × 8p (((p - 1)2)/4) × 8p
4g; ((p2 - 1)/2) × 8p 4h; ((p2 - 1)/2) × 8p 4i; ((p2 - 1)/2) × 8p p × 4j; p × 4k; p × 4l;
((p(p - 1))/2) × 8p ((p(p - 1))/2) × 8p ((p(p - 1))/2) × 8p
p × 4m; p × 4n; p × 4o; p2 × 8p
((p(p - 1))/2) × 8p ((p(p - 1))/2) × 8p ((p(p - 1))/2) × 8p
* p = 4n - 1 









































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