P222 No. 16 D21


Axes Coordinates Wyckoff positions
1a 1b 1c 1d 1e 1f 1g 1h 2i 2j 2k 2l
2m 2n 2o 2p 2q 2r 2s 2t 4u
I Maximal translationengleiche subgroups
[2] P211 (3) 1a 1a 1b 1c 1b 1c 1d 1d 2 × 1a 2 × 1c 2 × 1b 2 × 1d
[conventional setting]P121 c, a, b z, x, y 2e 2e 2e 2e 2e 2e 2e 2e 2 × 2e
[2] P121 (3) 1a 1c 1a 1b 1c 1d 1b 1d 2e 2e 2e 2e
2 × 1a 2 × 1b 2 × 1c 2 × 1d 2e 2e 2e 2e 2 × 2e
[2] P112 (3) 1a 1b 1c 1a 1d 1b 1c 1d 2e 2e 2e 2e
2e 2e 2e 2e 2 × 1a 2 × 1b 2 × 1c 2 × 1d 2 × 2e
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] F222 (22) 2a, 2b, 2c (1/2)x, (1/2)y, (1/2)z; +((1/2), 0, 0) 4a; 4b 8e 8f 8g 8h 8i 8j 4c; 4d 2 × 8e 16k 16k 2 × 8j
(22) 2 × 8f 16k 16k 2 × 8i 2 × 8g 16k 16k 2 × 8h 2 × 16k
[2] F222 (22) 2a, 2b, 2c (1/2)x + (1/4), (1/2)y, (1/2)z; +((1/2), 0, 0) 8e 4a; 4b 8h 8i 8f 8g 4c; 4d 8j 2 × 8e 16k 16k 2 × 8j
(22) 16k 2 × 8i 2 × 8f 16k 16k 2 × 8g 2 × 8h 16k 2 × 16k
[2] F222 (22) 2a, 2b, 2c (1/2)x, (1/2)y + (1/4), (1/2)z; +((1/2), 0, 0) 8f 8h 4a; 4b 8j 8e 4c; 4d 8g 8i 16k 2 × 8j 2 × 8e 16k
(22) 2 × 8f 16k 16k 2 × 8i 16k 2 × 8h 2 × 8g 16k 2 × 16k
[2] F222 (22) 2a, 2b, 2c (1/2)x, (1/2)y, (1/2)z + (1/4); +((1/2), 0, 0) 8g 8i 8j 4a; 4b 4c; 4d 8e 8f 8h 16k 2 × 8e 2 × 8j 16k
(22) 16k 2 × 8f 2 × 8i 16k 2 × 8g 16k 16k 2 × 8h 2 × 16k
[2] A222 (21) a, 2b, 2c x, (1/2)y, (1/2)z; +(0, (1/2), 0) 2a; 2b 2c; 2d 4e 4g 4f 4h 4k 4k 4i; 4j 8l 8l 2 × 4k
[conventional setting]C222 2b, 2c, a (1/2)y, (1/2)z, x; +((1/2), 0, 0) 2 × 4e 8l 2 × 4f 8l 2 × 4g 2 × 4h 8l 8l 2 × 8l
[2] A222 (21) a, 2b, 2c x, (1/2)y + (1/4), (1/2)z; +(0, (1/2), 0) 4e 4f 2a; 2b 4k 2c; 2d 4k 4g 4h 8l 2 × 4k 4i; 4j 8l
[conventional setting]C222 2b, 2c, a (1/2)y + (1/4), (1/2)z, x; +((1/2), 0, 0) 2 × 4e 8l 2 × 4f 8l 8l 8l 2 × 4g 2 × 4h 2 × 8l
[2] A222 (21) a, 2b, 2c x, (1/2)y, (1/2)z + (1/4); +(0, (1/2), 0) 4g 4h 4k 2a; 2b 4k 2c; 2d 4e 4f 8l 4i; 4j 2 × 4k 8l
[conventional setting]C222 2b, 2c, a (1/2)y, (1/2)z + (1/4), x; +((1/2), 0, 0) 8l 2 × 4e 8l 2 × 4f 2 × 4g 2 × 4h 8l 8l 2 × 8l
[2] A222 (21) a, 2b, 2c x, (1/2)y + (1/4), (1/2)z + (1/4); +(0, (1/2), 0) 4k 4k 4g 4e 4h 4f 2a; 2b 2c; 2d 2 × 4k 8l 8l 4i; 4j
[conventional setting]C222 2b, 2c, a (1/2)y + (1/4), (1/2)z + (1/4), x; +((1/2), 0, 0) 8l 2 × 4e 8l 2 × 4f 8l 8l 2 × 4g 2 × 4h 2 × 8l
[2] B222 (21) 2a, b, 2c (1/2)x, y, (1/2)z; +((1/2), 0, 0) 2a; 2b 4g 2c; 2d 4e 4h 4k 4f 4k 2 × 4g 8l 2 × 4h 8l
[conventional setting]C222 2c, 2a, b (1/2)z, (1/2)x, y; +(0, (1/2), 0) 4i; 4j 8l 8l 2 × 4k 2 × 4e 8l 2 × 4f 8l 2 × 8l
[2] B222 (21) 2a, b, 2c (1/2)x + (1/4), y, (1/2)z; +((1/2), 0, 0) 4g 2a; 2b 4h 4k 2c; 2d 4e 4k 4f 2 × 4g 8l 2 × 4h 8l
[conventional setting]C222 2c, 2a, b (1/2)z, (1/2)x + (1/4), y; +(0, (1/2), 0) 8l 2 × 4k 4i; 4j 8l 8l 2 × 4e 8l 2 × 4f 2 × 8l
[2] B222 (21) 2a, b, 2c (1/2)x, y, (1/2)z + (1/4); +((1/2), 0, 0) 4e 4k 4f 2a; 2b 4k 4g 2c; 2d 4h 8l 2 × 4g 8l 2 × 4h
[conventional setting]C222 2c, 2a, b (1/2)z + (1/4), (1/2)x, y; +(0, (1/2), 0) 8l 4i; 4j 2 × 4k 8l 2 × 4e 8l 2 × 4f 8l 2 × 8l
[2] B222 (21) 2a, b, 2c (1/2)x + (1/4), y, (1/2)z + (1/4); +((1/2), 0, 0) 4k 4e 4k 4g 4f 2a; 2b 4h 2c; 2d 8l 2 × 4g 8l 2 × 4h
[conventional setting]C222 2c, 2a, b (1/2)z + (1/4), (1/2)x + (1/4), y; +(0, (1/2), 0) 2 × 4k 8l 8l 4i; 4j 8l 2 × 4e 8l 2 × 4f 2 × 8l
[2] C222 (21) 2a, 2b, c (1/2)x, (1/2)y, z; +((1/2), 0, 0) 2a; 2b 4e 4g 2c; 2d 4k 4f 4h 4k 2 × 4e 2 × 4f 8l 8l
2 × 4g 2 × 4h 8l 8l 4i; 4j 8l 8l 2 × 4k 2 × 8l
[2] C222 (21) 2a, 2b, c (1/2)x + (1/4), (1/2)y, z; +((1/2), 0, 0) 4e 2a; 2b 4k 4f 4g 2c; 2d 4k 4h 2 × 4e 2 × 4f 8l 8l
8l 8l 2 × 4g 2 × 4h 8l 4i; 4j 2 × 4k 8l 2 × 8l
[2] C222 (21) 2a, 2b, c (1/2)x, (1/2)y + (1/4), z; +((1/2), 0, 0) 4g 4k 2a; 2b 4h 4e 4k 2c; 2d 4f 8l 8l 2 × 4e 2 × 4f
2 × 4g 2 × 4h 8l 8l 8l 2 × 4k 4i; 4j 8l 2 × 8l
[2] C222 (21) 2a, 2b, c (1/2)x + (1/4), (1/2)y + (1/4), z; +((1/2), 0, 0) 4k 4g 4e 4k 2a; 2b 4h 4f 2c; 2d 8l 8l 2 × 4e 2 × 4f
8l 8l 2 × 4g 2 × 4h 2 × 4k 8l 8l 4i; 4j 2 × 8l
[2] P2122 (17) 2a, b, c (1/2)x, y, z; +((1/2), 0, 0) 2a 2c 2a 2b 2d 2c 2b 2d 4e 4e 4e 4e
[conventional setting]P2221 b, c, 2a y, z, (1/2)x; +(0, 0, (1/2)) 2 × 2a 2 × 2b 4e 4e 4e 2 × 2c 4e 2 × 2d 2 × 4e
[2] P2122 (17) 2a, b, c (1/2)x + (1/4), y, z; +((1/2), 0, 0) 2c 2a 2d 2c 2a 2b 2d 2b 4e 4e 4e 4e
[conventional setting]P2221 b, c, 2a y, z, (1/2)x + (1/4); +(0, 0, (1/2)) 4e 4e 2 × 2a 2 × 2b 2 × 2c 4e 2 × 2d 4e 2 × 4e


Axes Coordinates Wyckoff positions
1a 1b 1c 1d 1e 1f 1g 1h 2i 2j 2k
2l 2m 2n 2o 2p 2q 2r 2s 2t 4u
[2] P2212 a, 2b, c x, (1/2)y, z; 2a 2b 2c 2a 2c 2b 2d 2d 4e 4e 2 × 2c
(17) +(0, (1/2), 0) 2 × 2d 4e 4e 4e 4e 2 × 2a 2 × 2b 4e 4e 2 × 4e
[conventional setting]P2221 c, a, 2b z, x, (1/2)y;
+(0, 0, (1/2))
[2] P2212 a, 2b, c x, (1/2)y + (1/4), z; 2c 2c 2a 2d 2b 2d 2a 2b 2 × 2c 2 × 2d 4e
(17) +(0, (1/2), 0) 4e 4e 4e 4e 4e 4e 4e 2 × 2a 2 × 2b 2 × 4e
[conventional setting]P2221 c, a, 2b z, x, (1/2)y + (1/4);
+(0, 0, (1/2))
[2] P2221 a, b, 2c x, y, (1/2)z; 2a 2a 2b 2c 2b 2d 2c 2d 2 × 2a 4e 2 × 2b
(17) +(0, 0, (1/2)) 4e 4e 2 × 2c 4e 2 × 2d 4e 4e 4e 4e 2 × 4e
[2] P2221 a, b, 2c x, y, (1/2)z + (1/4); 2c 2d 2c 2a 2d 2a 2b 2b 4e 2 × 2a 4e
(17) +(0, 0, (1/2)) 2 × 2b 2 × 2c 4e 2 × 2d 4e 4e 4e 4e 4e 2 × 4e
   Enlarged unit cell, isomorphic
[2] P222 2a, b, c (1/2)x, y, z; 1a; 1b 2i 1c; 1e 2d; 2f 2k 2j 1g; 1h 2l 2 × 2i 2 × 2j 2 × 2k
+((1/2), 0, 0) 2 × 2l 2m; 2o 2n; 2p 4u 4u 2q; 2r 4u 2s; 2t 4u 2 × 4u
[2] P222 2a, b, c (1/2)x + (1/4), y, z; 2i 1a; 1b 2k 2j 1c; 1e 1d; 1f 2l 1g; 1h 2 × 2i 2 × 2j 2 × 2k
+((1/2), 0, 0) 2 × 2l 4u 4u 2m; 2o 2n; 2p 4u 2q; 2r 4u 2s; 2t 2 × 4u
[3] P222 3a, b, c (1/3)x, y, z; 1a; 2i 1b; 2i 1c; 2k 1d; 2j 1e; 2k 1f; 2j 1g; 2l 1h; 2l 3 × 2i 3 × 2j 3 × 2k
±((1/3), 0, 0) 3 × 2l 2m; 4u 2n; 4u 2o; 4u 2p; 4u 2q; 4u 2r; 4u 2s; 4u 2t; 4u 3 × 4u
[p] P222 pa, b, c (1/p)x, y, z; 1a; 1b; 1c; 1d; 1e; 1f; 1g; 1h; p × 2i p × 2j p × 2k
+((u/p), 0, 0) ((p - 1)/2) × 2i ((p - 1)/2) × 2i ((p - 1)/2) × 2k ((p - 1)/2) × 2j ((p - 1)/2) × 2k ((p - 1)/2) × 2j ((p - 1)/2) × 2l ((p - 1)/2) × 2l
p = prime > 2; p × 2l 2m; 2n; 2o; 2p; 2q; 2r; 2s; 2t; p × 4u
u = 1, . . ., p - 1 ((p - 1)/2) × 4u ((p - 1)/2) × 4u ((p - 1)/2) × 4u ((p - 1)/2) × 4u ((p - 1)/2) × 4u ((p - 1)/2) × 4u ((p - 1)/2) × 4u ((p - 1)/2) × 4u
[2] P222 a, 2b, c x, (1/2)y, z; 1a; 1c 1b; 1e 2m 1d; 1g 2o 1f; 1h 2n 2p 2i; 2k 2j; 2l 4u
+(0, (1/2), 0) 4u 2 × 2m 2 × 2n 2 × 2o 2 × 2p 2q; 2s 2r; 2t 4u 4u 2 × 4u
[2] P222 a, 2b, c x, (1/2)y + (1/4), z; 2m 2o 1a; 1c 2n 1b; 1e 2p 1d; 1g 1f; 1h 4u 4u 2i; 2k
+(0, (1/2), 0) 2j; 2l 2 × 2m 2 × 2n 2 × 2o 2 × 2p 4u 4u 2q; 2s 2r; 2t 2 × 4u
[3] P222 a, 3b, c x, (1/3)y, z; 1a; 2m 1b; 2o 1c; 2m 1d; 2n 1e; 2o 1f; 2p 1g; 2n 1h; 2p 2i; 4u 2j; 4u 2k; 4u
±(0, (1/3), 0) 2l; 4u 3 × 2m 3 × 2n 3 × 2o 3 × 2p 2q; 4u 2r; 4u 2s; 4u 2t; 4u 3 × 4u
[p] P222 a, pb, c x, (1/p)y, z; 1a; 1b; 1c; 1d; 1e; 1f; 1g; 1h; 2i; 2j; 2k;
+(0, (u/p), 0) ((p - 1)/2) × 2m ((p - 1)/2) × 2o ((p - 1)/2) × 2m ((p - 1)/2) × 2n ((p - 1)/2) × 2o ((p - 1)/2) × 2p ((p - 1)/2) × 2n ((p - 1)/2) × 2p ((p - 1)/2) × 4u ((p - 1)/2) × 4u ((p - 1)/2) × 4u
p = prime > 2; 2l; p × 2m p × 2n p × 2o p × 2p 2q; 2r; 2s; 2t; p × 4u
u = 1, . . ., p - 1 ((p - 1)/2) × 4u ((p - 1)/2) × 4u ((p - 1)/2) × 4u ((p - 1)/2) × 4u ((p - 1)/2) × 4u
[2] P222 a, b, 2c x, y, (1/2)z; 1a; 1d 1b; 1f 1c; 1g 2q 1e; 1h 2r 2s 2t 2i; 2j 4u 2k; 2l
+(0, 0, (1/2)) 4u 2m; 2n 4u 2o; 2p 4u 2 × 2q 2 × 2r 2 × 2s 2 × 2t 2 × 4u
[2] P222 a, b, 2c x, y, (1/2)z + (1/4); 2q 2r 2s 1a; 1d 2t 1b; 1f 1c; 1g 1e; 1h 4u 2i; 2j 4u
+(0, 0, (1/2)) 2k; 2l 4u 2m; 2n 4u 2o; 2p 2 × 2q 2 × 2r 2 × 2s 2 × 2t 2 × 4u
[3] P222 a, b, 3c x, y, (1/3)z; 1a; 2q 1b; 2r 1c; 2s 1d; 2q 1e; 2t 1f; 2r 1g; 2s 1h; 2t 2i; 4u 2j; 4u 2k; 4u
±(0, 0, (1/3)) 2l; 4u 2m; 4u 2n; 4u 2o; 4u 2p; 4u 3 × 2q 3 × 2r 3 × 2s 3 × 2t 3 × 4u
[p] P222 a, b, pc x, y, (1/p)z; 1a; 1b; 1c; 1d; 1e; 1f; 1g; 1h; 2i; 2j; 2k;
+(0, 0, (u/p)) ((p - 1)/2) × 2q ((p - 1)/2) × 2r ((p - 1)/2) × 2s ((p - 1)/2) × 2q ((p - 1)/2) × 2t ((p - 1)/2) × 2r ((p - 1)/2) × 2s ((p - 1)/2) × 2t ((p - 1)/2) × 4u ((p - 1)/2) × 4u ((p - 1)/2) × 4u
p = prime > 2; 2l; 2m; 2n; 2o; 2p; p × 2q p × 2r p × 2s p × 2t p × 4u
u = 1, . . ., p - 1 ((p - 1)/2) × 4u ((p - 1)/2) × 4u ((p - 1)/2) × 4u ((p - 1)/2) × 4u ((p - 1)/2) × 4u









































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