P4/m No. 83 C4h1


Axes Coordinates Wyckoff positions
1a 1b 1c 1d 2e 2f 2g 2h 4i 4j 4k
8l
I Maximal translationengleiche subgroups
[2] P-4 (81) 1a 1b 1c 1d 2g 2g 2e 2f 2 × 2g 4h 4h
2 × 4h
[2] P4 (75) 1a 1a 1b 1b 2c 2c 2 × 1a 2 × 1b 2 × 2c 4d 4d
2 × 4d
[2] P112/m (10) 1a 1b 1g 1h 1c; 1d 1e; 1f 2i 2l 2j; 2k 2 × 2m 2 × 2n
2 × 4o
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] I4/m (87) a - b, a + b, 2c (1/2)(x - y), (1/2)(x + y), (1/2)z; 2a; 2b 4e 4c 4d 8h 8f 2 × 4e 8g 16i 2 × 8h 16i
+(0, 0, (1/2)) 2 × 16i
[2] I4/m (87) a - b, a + b, 2c (1/2)(x - y) + (1/2), (1/2)(x + y), (1/2)z; 4c 4d 2a; 2b 4e 8h 8f 8g 2 × 4e 16i 2 × 8h 16i
+(0, 0, (1/2)) 2 × 16i
[2] I4/m (87) a - b, a + b, 2c (1/2)(x - y), (1/2)(x + y), (1/2)z + (1/4); 4e 2a; 2b 4d 4c 8f 8h 2 × 4e 8g 16i 16i 2 × 8h
+(0, 0, (1/2)) 2 × 16i
[2] I4/m (87) a - b, a + b, 2c (1/2)(x - y) + (1/2), (1/2)(x + y), 4d 4c 4e 2a; 2b 8f 8h 8g 2 × 4e 16i 16i 2 × 8h
(1/2)z + (1/4); +(0, 0, (1/2)) 2 × 16i
[2] P4/n (85) a - b, a + b, c origin 1 : (1/2)(x - y), 2a 2b 2c 2c 4d 4e 4f 2 × 2c 8g 8g 8g
(1/2)(x + y), z; +((1/2), (1/2), 0) 2 × 8g
origin 2 : (1/2)(x - y) - (1/4),
(1/2)(x + y) + (1/4), z; +((1/2), (1/2), 0)
[2] P4/n (85) a - b, a + b, c origin 1 : (1/2)(x - y) + (1/2), 2c 2c 2a 2b 4d 4e 2 × 2c 4f 8g 8g 8g
(1/2)(x + y), z; +((1/2), (1/2), 0) 2 × 8g
origin 2 : (1/2)(x - y) + (1/4),
(1/2)(x + y) + (1/4), z; +((1/2), (1/2), 0)
[2] P42/m (84) a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a 2e 2b 2f 2c; 2d 4i 4g 4h 2 × 4i 2 × 4j 8k
2 × 8k
[2] P42/m (84) 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 8k 2 × 4j
2 × 8k


Axes Coordinates Wyckoff positions
1a 1b 1c 1d 2e 2f 2g 2h
4i 4j 4k 8l
   Enlarged unit cell, isomorphic
[2] P4/m 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 8l 2 × 8l
[2] P4/m 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 8l 4j; 4k 2 × 8l
[3] P4/m 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; 8l 4k; 8l 3 × 8l
[p] P4/m a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 1a; 1b; 1c; 1d; 2e; 2f; p × 2g p × 2h
p = prime > 2; u = 1, . . ., p - 1 ((p - 1)/2) × 2g ((p - 1)/2) × 2g ((p - 1)/2) × 2h ((p - 1)/2) × 2h ((p - 1)/2) × 4i ((p - 1)/2) × 4i
p × 4i 4j; 4k; p × 8l
((p - 1)/2) × 8l ((p - 1)/2) × 8l
[2] P4/m a - b, a + b, c (1/2)(x - y), (1/2)(x + y), z; 1a; 1c 1b; 1d 2e 2f 4j 4k 2g; 2h 4i
+((1/2), (1/2), 0) 8l 2 × 4j 2 × 4k 2 × 8l
[2] P4/m a - b, a + b, c (1/2)(x - y) + (1/2), (1/2)(x + y), z; 2e 2f 1a; 1c 1b; 1d 4j 4k 4i 2g; 2h
+((1/2), (1/2), 0) 8l 2 × 4j 2 × 4k 2 × 8l
[5] P4/m a + 2b, -2a + b, c (1/5)(x + 2y), (1/5)(-2x + y), z; 1a; 4j 1b; 4k 1c; 4j 1d; 4k 2e; 2 × 4j 2f; 2 × 4k 2g; 8l 2h; 8l
±((1/5), (3/5), 0); ±((2/5), (1/5), 0) 4i; 2 × 8l 5 × 4j 5 × 4k 5 × 8l
[5] P4/m a - 2b, 2a + b, c (1/5)(x - 2y), (1/5)(2x + y), z; 1a; 4j 1b; 4k 1c; 4j 1d; 4k 2e; 2 × 4j 2f; 2 × 4k 2g; 8l 2h; 8l
±((1/5), (2/5), 0); ±((3/5), (1/5), 0) 4i; 2 × 8l 5 × 4j 5 × 4k 5 × 8l
[p] P4/m qa - rb, (1/p)(qx - ry), (1/p)(rx + qy), z; 1a; 1b; 1c; 1d; 2e; 2f; 2g; 2h;
ra + qb, c +((uq/p), (ur/p), 0) ((p - 1)/4) × 4j ((p - 1)/4) × 4k ((p - 1)/4) × 4j ((p - 1)/4) × 4k ((p - 1)/2) × 4j ((p - 1)/2) × 4k ((p - 1)/4) × 8l ((p - 1)/4) × 8l
p = q2 + r2 = prime = 4n + 1; 4i; p × 4j p × 4k p × 8l
q = 2n + 1 ≥ 1; r = ± 2n'≠ 0; ((p - 1)/2) × 8l
u = 1, . . ., p - 1
[9] P4/m 3a, 3b, c (1/3)x, (1/3)y, z; 1a; 2 × 4j 1b; 2 × 4k 1c; 2 × 4j 1d; 2 × 4k 2e; 4 × 4j 2f; 4 × 4k 2g; 2 × 8l 2h; 2 × 8l
±((1/3), 0, 0); ±(0, (1/3), 0); 4i; 4 × 8l 9 × 4j 9 × 4k 9 × 8l
±((1/3), (1/3), 0); ±((1/3), (2/3), 0)
[p2] P4/m pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) 1a; 1b; 1c; 1d; 2e; 2f; 2g; 2h;
p = prime = 4n - 1; ((p2 - 1)/4) × 4j ((p2 - 1)/4) × 4k ((p2 - 1)/4) × 4j ((p2 - 1)/4) × 4k ((p2 - 1)/2) × 4j ((p2 - 1)/2) × 4k ((p2 - 1)/4) × 8l ((p2 - 1)/4) × 8l
u, v = 1, . . ., p - 1 4i; p2 × 4j p2 × 4k p2 × 8l
((p2 - 1)/2) × 8l









































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