222 222 Orthorhombic No. 13 222 Patterson symmetry mmm

Origin at 222

 Asymmetric unit 0 ≤ x; 0 ≤ y; 0 ≤ z ≤ 1

Symmetry operations

 (1)  1      (1 | 0, 0, 0) (2)  2   0, 0, z      (2z | 0, 0, 0) (3)  2   0, y, 0      (2y | 0, 0, 0) (4)  2   x, 0, 0      (2x | 0, 0, 0)

Generators selected (1); t(0, 0, 1); (2); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 4 h 1
 (1) x, y, z (2) -x, -y, z (3) -x, y, -z (4) x, -y, -z
no conditions
Special: no extra conditions
 2 g . . 2
 0, 0, z 0, 0, -z
 2 f . 2 .
 0, y, 1/2 0, -y, 1/2
 2 e . 2 .
 0, y, 0 0, -y, 0
 2 d 2 . .
 x, 0, 1/2 -x, 0, 1/2
 2 c 2 . .
 x, 0, 0 -x, 0, 0
 1 b 2 2 2
 0, 0, 1/2
 1 a 2 2 2
 0, 0, 0

Symmetry of special projections

 Along [001]   2mmOrigin at 0, 0, z Along [100]   2mma' = c   Origin at x, 0, 0 Along [010]   2mma' = c   Origin at 0, y, 0

Maximal non-isotypic non-enantiomorphic subgroups

 I [2] 112 (8) 1; 2 [2] 121 (211, 3) 1; 3 [2] 211 (3) 1; 4
 IIa none
 IIb [2] 2221 (c' = 2c) (14)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [2] 222 (c' = 2c) (13)

Minimal non-isotypic non-enantiomorphic supergroups

 I [2] mmm (20); [2] ccm (21); [2] 422 (30); [2] 4222 (32); [2] -42m (37); [2] -42c (38); [3] 622 (62); [3] 6222 (64); [3] 6422 (66)
 II none