P42/m No. 84 C4h2


Axes Coordinates Wyckoff positions
2a 2b 2c 2d 2e 2f 4g 4h
4i 4j 8k
I Maximal translationengleiche subgroups
[2] P-4 (81) x, y, z + (1/4) 2e 2f 2g 2g 1a; 1b 1c; 1d 2 × 2e 2 × 2f
2 × 2g 4h 2 × 4h
[2] P42 (77) 2a 2b 2c 2c 2a 2b 2 × 2a 2 × 2b
2 × 2c 4d 2 × 4d
[2] P112/m 1a; 1b 1g; 1h 1d; 1f 1c; 1e 2i 2l 2 × 2i 2 × 2l
  (10) 2j; 2k 2m; 2n 2 × 4o
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] P42/n a - b, a + b, c origin 1 : (1/2)(x - y), 4f 4e 4d 4c 2a; 2b 4e 2 × 4f 2 × 4e
  (86) (1/2)(x + y), z + (1/4); +((1/2), (1/2), 0) 8g 8g 2 × 8g
origin 2 : (1/2)(x - y) + (1/4),
(1/2)(x + y) + (1/4), z; +((1/2), (1/2), 0)
[2] P42/n a - b, a + b, c origin 1 : (1/2)(x - y) + (1/2), 4e 4f 4c 4d 4e 2a; 2b 2 × 4e 2 × 4f
  (86) (1/2)(x + y), z + (1/4); +((1/2), (1/2), 0) 8g 8g 2 × 8g
origin 2 : (1/2)(x - y) - (1/4),
(1/2)(x + y) + (1/4), z; +((1/2), (1/2), 0)
   Enlarged unit cell, isomorphic
[3] P42/m 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; 8k 3 × 8k
[p] P42/m a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 2a; 2b; 2c; 2d; 2e; 2f; p × 4g p × 4h
p = prime > 2; u = 1, . . ., p - 1 ((p - 1)/2) × 4g ((p - 1)/2) × 4h ((p - 1)/2) × 4i ((p - 1)/2) × 4i ((p - 1)/2) × 4g ((p - 1)/2) × 4h
p × 4i 4j; p × 8k
((p - 1)/2) × 8k
[2] P42/m a - b, a + b, c (1/2)(x - y), (1/2)(x + y), z; 2a; 2b 2c; 2d 4j 4j 2e; 2f 4i 4g; 4h 2 × 4i
+((1/2), (1/2), 0) 8k 2 × 4j 2 × 8k
[2] P42/m a - b, a + b, c (1/2)(x - y) + (1/2), (1/2)(x + y), z; 2c; 2d 2a; 2b 4j 4j 4i 2e; 2f 2 × 4i 4g; 4h
+((1/2), (1/2), 0) 8k 2 × 4j 2 × 8k
[5] P42/m a + 2b, (1/5)(x + 2y), (1/5)(-2x + y), z; 2a; 2 × 4j 2b; 2 × 4j 2c; 2 × 4j 2d; 2 × 4j 2e; 8k 2f; 8k 4g; 2 × 8k 4h; 2 × 8k
-2a + b, c ±((1/5), (3/5), 0); ±((2/5), (1/5), 0) 4i; 2 × 8k 5 × 4j 5 × 8k
[5] P42/m a - 2b, (1/5)(x - 2y), (1/5)(2x + y), z; 2a; 2 × 4j 2b; 2 × 4j 2c; 2 × 4j 2d; 2 × 4j 2e; 8k 2f; 8k 4g; 2 × 8k 4h; 2 × 8k
2a + b, c ±((1/5), (2/5), 0); ±((3/5), (1/5), 0) 4i; 2 × 8k 5 × 4j 5 × 8k
[p] P42/m qa - rb, (1/p)(qx - ry), (1/p)(rx + qy), z; 2a; 2b; 2c; 2d; 2e; 2f; 4g; 4h;
ra + qb, c +((uq/p), (ur/p), 0) ((p - 1)/2) × 4j ((p - 1)/2) × 4j ((p - 1)/2) × 4j ((p - 1)/2) × 4j ((p - 1)/4) × 8k ((p - 1)/4) × 8k ((p - 1)/2) × 8k ((p - 1)/2) × 8k
p = q2 + r2 = prime = 4n + 1; 4i; p × 4j p × 8k
q = 2n + 1 ≥ 1; r = ± 2n'≠ 0; ((p - 1)/2) × 8k
u = 1, . . ., p - 1
[9] P42/m 3a, 3b, c (1/3)x, (1/3)y, z; ±((1/3), 0, 0); 2a; 4 × 4j 2b; 4 × 4j 2c; 4 × 4j 2d; 4 × 4j 2e; 2 × 8k 2f; 2 × 8k 4g; 4 × 8k 4h; 4 × 8k
±(0, (1/3), 0); ±((1/3), (1/3), 0); ±((1/3), (2/3), 0) 4i; 4 × 8k 9 × 4j 9 × 8k
[p2] P42/m pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) 2a; 2b; 2c; 2d; 2e; 2f; 4g; 4h;
p = prime = 4n - 1; ((p2 - 1)/2) × 4j ((p2 - 1)/2) × 4j ((p2 - 1)/2) × 4j ((p2 - 1)/2) × 4j ((p2 - 1)/4) × 8k ((p2 - 1)/4) × 8k ((p2 - 1)/2) × 8k ((p2 - 1)/2) × 8k
u, v = 1, . . ., p - 1 4i; p2 × 4j p2 × 8k
((p2 - 1)/2) × 8k









































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