P-4m2 No. 115 D2d5


Axes Coordinates Wyckoff positions
1a 1b 1c 1d 2e 2f 2g 4h
4i 4j 4k 8l
I Maximal translationengleiche subgroups
[2] P-4 (81) 1a 1c 1d 1b 2e 2f 2g 4h
4h 4h 4h 2 × 4h
[2] Pmm2 1a 1d 1d 1a 2 × 1a 2 × 1d 1b; 1c 4i
(25) 4i 2e; 2g 2f; 2h 2 × 4i
[2] C222 a - b, (1/2)(x - y), (1/2)(x + y), z 2a 2b 2c 2d 4i 4j 4k 4e; 4g
(21) a + b, c 4f; 4h 8l 8l 2 × 8l
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] I-42m a - b, (1/2)(x - y), (1/2)(x + y), (1/2)z; 2a; 2b 4c 4d 4e 2 × 4e 8h 8i 8f; 8g
(121) a + b, 2c +(0, 0, (1/2)) 16j 2 × 8i 16j 2 × 16j
[2] I-42m a - b, (1/2)(x - y), (1/2)(x + y), 4e 4d 4c 2a; 2b 2 × 4e 8h 8i 16j
(121) a + b, 2c (1/2)z + (1/4); +(0, 0, (1/2)) 8f; 8g 2 × 8i 16j 2 × 16j
[2] I-42m a - b, (1/2)(x - y) + (1/2), (1/2)(x + y), (1/2)z; 4c 2a; 2b 4e 4d 8h 2 × 4e 8i 8f; 8g
(121) a + b, 2c +(0, 0, (1/2)) 16j 16j 2 × 8i 2 × 16j
[2] I-42m a - b, (1/2)(x - y) + (1/2), (1/2)(x + y), 4d 4e 2a; 2b 4c 8h 2 × 4e 8i 16j
(121) a + b, 2c (1/2)z + (1/4); +(0, 0, (1/2)) 8f; 8g 16j 2 × 8i 2 × 16j
[2] P-4c2 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2c 2d 2b 2a 4g 4h 4i 8j
(116) 4e; 4f 8j 8j 2 × 8j
[2] P-4c2 a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 2a 2b 2d 2c 4g 4h 4i 4e; 4f
(116) 8j 8j 8j 2 × 8j
[2] P-421m a - b, (1/2)(x - y), (1/2)(x + y), z; 2a 2c 2c 2b 4d 2 × 2c 4e 8f
(113) a + b, c +((1/2), (1/2), 0) 8f 8f 2 × 4e 2 × 8f
[2] P-421m a - b, (1/2)(x - y) + (1/2), (1/2)(x + y), z; 2c 2a 2b 2c 2 × 2c 4d 4e 8f
(113) a + b, c +((1/2), (1/2), 0) 8f 2 × 4e 8f 2 × 8f
[2] P-42m a - b, (1/2)(x - y), (1/2)(x + y), z; 1a; 1d 2e 2f 1b; 1c 2g; 2h 4m 4n 4i; 4l
(111) a + b, c +((1/2), (1/2), 0) 4j; 4k 2 × 4n 8o 2 × 8o
[2] P-42m a - b, (1/2)(x - y) + (1/2), (1/2)(x + y), z; 2e 1a; 1d 1b; 1c 2f 4m 2g; 2h 4n 4i; 4l
(111) a + b, c +((1/2), (1/2), 0) 4j; 4k 8o 2 × 4n 2 × 8o
   Enlarged unit cell, isomorphic
[2] P-4m2 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 1a; 1d 1b; 1c 2f 2e 2 × 2e 2 × 2f 2 × 2g 4h; 4i
8l 2 × 4j 2 × 4k 2 × 8l
[2] P-4m2 a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 2e 2f 1b; 1c 1a; 1d 2 × 2e 2 × 2f 2 × 2g 8l
4h; 4i 2 × 4j 2 × 4k 2 × 8l
[3] P-4m2 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 1a; 2e 1b; 2f 1c; 2f 1d; 2e 3 × 2e 3 × 2f 3 × 2g 4h; 8l
4i; 8l 3 × 4j 3 × 4k 3 × 8l
[p] P-4m2 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 1a; ((p - 1)/2) × 2e 1b; ((p - 1)/2) × 2f 1c; ((p - 1)/2) × 2f 1d; ((p - 1)/2) × 2e p × 2e p × 2f p × 2g 4h; ((p - 1)/2) × 8l
p = prime > 2; u = 1, . . ., p - 1 4i; ((p - 1)/2) × 8l p × 4j p × 4k p × 8l


Axes Coordinates Wyckoff positions
1a 1b 1c 1d 2e 2f
2g 4h 4i 4j 4k 8l
[9] P-4m2 3a, 3b, c (1/3)x, (1/3)y, z; 1a; 4h; 4j 1b; 4h; 4k 1c; 4i; 4k 1d; 4i; 4j 2e; 2 × 4j; 8l 2f; 2 × 4 k; 8l
±((1/3), 0, 0); ±(0, (1/3), 0); 2g; 4j; 4k; 8l 3 × 4h; 3 × 8l 3 × 4i; 3 × 8l 3 × 4j; 3 × 8l 3 × 4k; 3 × 8l 9 × 8l
±((1/3), (1/3), 0); ±((1/3), (2/3), 0)
[p2] P-4m2 pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) 1a; ((p - 1)/2) × 4h; 1b; ((p - 1)/2) × 4h; 1c; ((p - 1)/2) × 4i; 1d; ((p - 1)/2) × 4i; 2e; (p - 1) × 4j; 2f; (p - 1) × 4k;
p = prime > 2; ((p - 1)/2) × 4j; ((p - 1)/2) × 4k; ((p - 1)/2) × 4k; ((p - 1)/2) × 4j; (((p - 1)2)/4) × 8l (((p - 1)2)/4) × 8l
u, v = 1, . . ., p - 1 (((p - 1)(p - 3))/8) × 8l (((p - 1)(p - 3))/8) × 8l (((p - 1)(p - 3))/8) × 8l (((p - 1)(p - 3))/8) × 8l
2g; ((p - 1)/2) × 4j; p × 4h; p × 4i; p × 4j; p × 4k; ((p(p - 1))/2) × 8l p2 × 8l
((p - 1)/2) × 4k; ((p(p - 1))/2) × 8l ((p(p - 1))/2) × 8l ((p(p - 1))/2) × 8l
(((p - 1)2)/4) × 8l









































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