P422 No. 89 D41


Axes Coordinates Wyckoff positions
1a 1b 1c 1d 2e 2f 2g 2h 4i 4j 4k
4l 4m 4n 4o 8p
I Maximal translationengleiche subgroups
[2] P4 (75) 1a 1a 1b 1b 2c 2c 2 × 1a 2 × 1b 2 × 2c 4d 4d
4d 4d 4d 4d 2 × 4d
[2] P222 (16) 1a 1d 1e 1h 1b; 1c 1f; 1g 2q 2t 2r; 2s 4u 4u
2i; 2m 2l; 2p 2j; 2n 2k; 2o 2 × 4u
[2] C222 a - b, a + b, c (1/2)(x - y), (1/2)(x + y), z 2a 2d 2b 2c 4k 4k 4i 4j 2 × 4k 4e; 4g 4f; 4h
  (21) 8l 8l 8l 8l 2 × 8l
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] I422 a - b, a + b, 2c (1/2)(x - y), (1/2)(x + y), (1/2)z; 2a; 2b 4e 4c 4d 8g 8j 2 × 4e 8f 16k 8h; 8i 16k
  (97) +(0, 0, (1/2)) 2 × 8g 2 × 8j 16k 16k 2 × 16k
[2] I422 a - b, a + b, 2c (1/2)(x - y) + (1/2), (1/2)(x + y), (1/2)z; 4c 4d 2a; 2b 4e 8g 8j 8f 2 × 4e 16k 8h; 8i 16k
  (97) +(0, 0, (1/2)) 16k 16k 2 × 8j 2 × 8g 2 × 16k
[2] I422 a - b, a + b, 2c (1/2)(x - y), (1/2)(x + y), 4e 2a; 2b 4d 4c 8j 8g 2 × 4e 8f 16k 16k 8h; 8i
  (97) (1/2)z + (1/4); +(0, 0, (1/2)) 16k 16k 2 × 8g 2 × 8j 2 × 16k
[2] I422 a - b, a + b, 2c (1/2)(x - y) + (1/2), (1/2)(x + y), 4d 4c 4e 2a; 2b 8j 8g 8f 2 × 4e 16k 16k 8h; 8i
  (97) (1/2)z + (1/4); +(0, 0, (1/2)) 2 × 8j 2 × 8g 16k 16k 2 × 16k
[2] P4222 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a 2e 2b 2f 2c; 2d 4i 4g 4h 2 × 4i 8p 4n; 4o
  (93) 4j; 4l 8p 8p 4k; 4m 2 × 8p
[2] P4222 a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 2e 2a 2f 2b 4i 2c; 2d 4g 4h 2 × 4i 4n; 4o 8p
  (93) 8p 4k; 4m 4j; 4l 8p 2 × 8p
[2] P4212 a - b, a + b, c (1/2)(x - y), (1/2)(x + y), z; 2a 2b 2c 2c 4e 4f 4d 2 × 2c 8g 8g 8g
  (90) +((1/2), (1/2), 0) 2 × 4e 8g 2 × 4f 8g 2 × 8g
[2] P4212 a - b, a + b, c (1/2)(x - y) + (1/2), (1/2)(x + y), z; 2c 2c 2a 2b 4e 4f 2 × 2c 4d 8g 8g 8g
  (90) +((1/2), (1/2), 0) 8g 2 × 4f 8g 2 × 4e 2 × 8g
   Enlarged unit cell, isomorphic
[2] P422 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 1a; 1b 2g 1c; 1d 2h 2e; 2f 4i 2 × 2g 2 × 2h 2 × 4i 4j; 4k 8p
4l; 4n 8p 8p 4m; 4o 2 × 8p
[2] P422 a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 2g 1a; 1b 2h 1c; 1d 4i 2e; 2f 2 × 2g 2 × 2h 2 × 4i 8p 4j; 4k
8p 4m; 4o 4l; 4n 8p 2 × 8p
[3] P422 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 1a; 2g 1b; 2g 1c; 2h 1d; 2h 2e; 4i 2f; 4i 3 × 2g 3 × 2h 3 × 4i 4j; 8p 4k; 8p
4l; 8p 4m; 8p 4n; 8p 4o; 8p 3 × 8p


Axes Coordinates Wyckoff positions
  1a 1b 1c 1d 2e 2f 2g
2h 4i 4j 4k 4l 4m
4n 4o 8p
[p] P422 a, b, pc x, y, (1/p)z; 1a; ((p - 1)/2) × 2g 1b; ((p - 1)/2) × 2g 1c; ((p - 1)/2) × 2h 1d; ((p - 1)/2) × 2h 2e; ((p - 1)/2) × 4i 2f; ((p - 1)/2) × 4i p × 2g
+(0, 0, (u/p)) p × 2h p × 4i 4j; ((p - 1)/2) × 8p 4k; ((p - 1)/2) × 8p 4l; ((p - 1)/2) × 8p 4m; ((p - 1)/2) × 8p
p = prime > 2; 4n; ((p - 1)/2) × 8p 4o; ((p - 1)/2) × 8p p × 8p
u = 1, . . ., p - 1
[2] P422 a - b, (1/2)(x - y), 1a; 1c 1b; 1d 2e 2f 4j 4k 2g; 2h
a + b, c (1/2)(x + y), z; 4i 8p 4l; 4o 4m; 4n 2 × 4j 8p
+((1/2), (1/2), 0) 2 × 4k 8p 2 × 8p
[2] P422 a - b, (1/2)(x - y) + (1/2), 2e 2f 1a; 1c 1b; 1d 4j 4k 4i
a + b, c (1/2)(x + y), z; 2g; 2h 8p 4l; 4o 4m; 4n 8p 2 × 4k
+((1/2), (1/2), 0) 8p 2 × 4j 2 × 8p
[9] P422 3a, 3b, c (1/3)x, (1/3)y, z; 1a; 4j; 4l 1b; 4k; 4n 1c; 4j; 4o 1d; 4k; 4m 2e; 4l; 4o; 8p 2f; 4m; 4n; 8p 2g; 2 × 8p
±((1/3), 0, 0); 2h; 2 × 8p 4i; 4 × 8p 3 × 4j; 3 × 8p 3 × 4k; 3 × 8p 3 × 4l; 3 × 8p 3 × 4m; 3 × 8p
±(0, (1/3), 0); 3 × 4n; 3 × 8p 3 × 4o; 3 × 8p 9 × 8p
±((1/3), (1/3), 0);
±((1/3), (2/3), 0)
[p2] P422 pa, pb, c (1/p)x, (1/p)y, z; 1a; ((p - 1)/2) × 4j; 1b; ((p - 1)/2) × 4k; 1c; ((p - 1)/2) × 4j; 1d; ((p - 1)/2) × 4k; 2e; ((p - 1)/2) × 4l; 2f; ((p - 1)/2) × 4m; 2g; ((p2 - 1)/4) × 8p
+((u/p), (v/p), 0) ((p - 1)/2) × 4l; ((p - 1)/2) × 4n; ((p - 1)/2) × 4o; ((p - 1)/2) × 4m; ((p - 1)/2) × 4o; ((p - 1)/2) × 4n;
p = prime > 2; (((p - 1)(p - 3))/8) × 8p (((p - 1)(p - 3))/8) × 8p (((p - 1)(p - 3))/8) × 8p (((p - 1)(p - 3))/8) × 8p (((p - 1)2)/4) × 8p (((p - 1)2)/4) × 8p
u, v = 1, . . ., p - 1 2h; ((p2 - 1)/4) × 8p 4i; ((p2 - 1)/2) × 8p p × 4j; p × 4k; p × 4l; p × 4m;
((p(p - 1))/2) × 8p ((p(p - 1))/2) × 8p ((p(p - 1))/2) × 8p ((p(p - 1))/2) × 8p
p × 4n; p × 4o; p2 × 8p
((p(p - 1))/2) × 8p ((p(p - 1))/2) × 8p









































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