F222 No. 22 D27


Axes Coordinates Wyckoff positions
4a 4b 4c 4d 8e 8f 8g 8h 8i 8j 16k
I Maximal translationengleiche subgroups
[2] C211 (5) a, b, x, y + z, 2z 2a 2a 2b 2b 2 × 2a 4c 4c 4c 4c 2 × 2b 2 × 4c
(1/2)(-b + c)
[conventional setting]C121 b, -a, y + z, -x, 2z
(1/2)(-b + c)
[2] C121 (5) a, b, x + z, y, 2z 2a 2a 2b 2b 4c 2 × 2a 4c 4c 2 × 2b 4c 2 × 4c
(1/2)(-a + c)
[2] A112 (5) (1/2)(a - b), 2x, x + y, z 2a 2a 2b 2b 4c 4c 2 × 2a 2 × 2b 4c 4c 2 × 4c
b, c
II Maximal klassengleiche subgroups
   Loss of centring translations
[2] A222 (21) 2a; 2c 2b; 2d 4k 4k 4i; 4j 4e; 4f 4g; 4h 8l 8l 2 × 4k 2 × 8l
[conventional setting]C222 b, c, a y, z, x
[2] A222 (21) x + (1/4), y + (1/4), z + (1/4) 4k 4k 2b; 2d 2a; 2c 2 × 4k 8l 8l 4g; 4h 4e; 4f 4i; 4j 2 × 8l
[conventional setting]C222 b, c, a y + (1/4), z + (1/4), x + (1/4)
[2] B222 (21) 2a; 2c 2b; 2d 4k 4k 4g; 4h 4i; 4j 4e; 4f 8l 2 × 4k 8l 2 × 8l
[conventional setting]C222 c, a, b z, x, y
[2] B222 (21) x + (1/4), y + (1/4), z + (1/4) 4k 4k 2b; 2d 2a; 2c 8l 2 × 4k 8l 4e; 4f 4i; 4j 4g; 4h 2 × 8l
[conventional setting]C222 c, a, b z + (1/4), x + (1/4), y + (1/4)
[2] C222 (21) 2a; 2c 2b; 2d 4k 4k 4e; 4f 4g; 4h 4i; 4j 2 × 4k 8l 8l 2 × 8l
[2] C222 (21) x + (1/4), y + (1/4), z + (1/4) 4k 4k 2b; 2d 2a; 2c 8l 8l 2 × 4k 4i; 4j 4g; 4h 4e; 4f 2 × 8l
[2] A2122 (20) x, y + (1/4), z 4a 4a 4b 4b 8c 2 × 4a 8c 2 × 4b 8c 8c 2 × 8c
[conventional setting]C2221 b, c, a y + (1/4), z, x
[2] A2122 (20) x + (1/4), y, z + (1/4) 4b 4b 4a 4a 8c 8c 2 × 4b 8c 2 × 4a 8c 2 × 8c
[conventional setting]C2221 b, c, a y, z + (1/4), x + (1/4)
[2] B2212 (20) x, y, z + (1/4) 4a 4a 4b 4b 8c 8c 2 × 4a 8c 8c 2 × 4b 2 × 8c
[conventional setting]C2221 c, a, b z + (1/4), x, y
[2] B2212 (20) x + (1/4), y + (1/4), z 4b 4b 4a 4a 2 × 4b 8c 8c 2 × 4a 8c 8c 2 × 8c
[conventional setting]C2221 c, a, b z, x + (1/4), y + (1/4)
[2] C2221 (20) x + (1/4), y, z 4a 4a 4b 4b 2 × 4a 8c 8c 8c 2 × 4b 8c 2 × 8c
[2] C2221 (20) x, y + (1/4), z + (1/4) 4b 4b 4a 4a 8c 2 × 4b 8c 8c 8c 2 × 4a 2 × 8c
   Enlarged unit cell, isomorphic
[3] F222 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) 4a; 8e 4b; 8e 4d; 8j 4c; 8j 3 × 8e 8f; 16k 8g; 16k 8h; 16k 8i; 16k 3 × 8j 3 × 16k
[p] F222 pa, b, c (1/p)x, y, z; +((u/p), 0, 0) 4a; 4b; 4c(d*); 4d(c*); p × 8e 8f; 8g; 8h; 8i; p × 8j p × 16k
p = prime > 2; ((p - 1)/2) × 8e ((p - 1)/2) × 8e ((p - 1)/2) × 8j ((p - 1)/2) × 8j ((p - 1)/2) × ((p - 1)/2) × ((p - 1)/2) × ((p - 1)/2) ×
u = 1, . . ., p - 1 16k 16k 16k 16k
[3] F222 a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) 4a; 8 f 4b; 8f 4d; 8i 4c; 8i 8e; 16k 3 × 8f 8g; 16k 8h; 16k 3 × 8i 8j; 16k 3 × 16k
[p] F222 a, pb, c x, (1/p)y, z; +(0, (u/p), 0) 4a; 4b; 4c(d*); 4d(c*); 8e; p × 8f 8g; 8h; p × 8i 8j; p × 16k
p = prime > 2; ((p - 1)/2) × 8f ((p - 1)/2) × 8f ((p - 1)/2) × 8i ((p - 1)/2) × 8i ((p - 1)/2) × ((p - 1)/2) × ((p - 1)/2) × ((p - 1)/2) ×
u = 1, . . ., p - 1 16k 16k 16k 16k
[3] F222 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 4a; 8g 4b; 8g 4d; 8h 4c; 8h 8e; 16k 8 f; 16k 3 × 8g 3 × 8h 8i; 16k 8j; 16k 3 × 16k
[p] F222 a, b, pc x, y, (1/p)y; +(0, 0, (u/p)) 4a; 4b; 4c(d*); 4d(c*); 8e; 8f; p × 8g p × 8h 8i; 8j; p × 16k
p = prime > 2; ((p - 1)/2) × 8g ((p - 1)/2) × 8g ((p - 1)/2) × 8h ((p - 1)/2) × 8h ((p - 1)/2) × ((p - 1)/2) × ((p - 1)/2) × ((p - 1)/2) ×
u = 1, . . ., p - 1 16k 16k 16k 16k
* p = 4n - 1









































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