mcm mmm Orthorhombic No. 22 2/m2/c21/m Patterson symmetry mmm

Origin at centre (2/m) at 2/mc21

 Asymmetric unit 0 ≤ x; 0 ≤ z ≤ 1/4

Symmetry operations

 (1)  1 (2)  2   0, y, 1/4 (3)  2   x, 0, 0 (4)  2(1/2)   0, 0, z (5)  -1   0, 0, 0 (6)  c   x, 0, z (7)  m   0, y, z (8)  m   x, y, 1/4

Generators selected (1); t(0, 0, 1); (2); (3); (5)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 8 f 1
 (1) x, y, z (2) -x, y, -z + 1/2 (3) x, -y, -z (4) -x, -y, z + 1/2 (5) -x, -y, -z (6) x, -y, z + 1/2 (7) -x, y, z (8) x, y, -z + 1/2
no conditions
Special: no extra conditions
 4 e . . m
 x, y, 1/4 -x, y, 1/4 x, -y, 3/4 -x, -y, 3/4
 4 d m . .
 0, y, z 0, y, -z + 1/2 0, -y, -z 0, -y, z + 1/2
 4 c 2 . .
 x, 0, 0 -x, 0, 1/2 -x, 0, 0 x, 0, 1/2
 2 b m 2 m
 0, y, 1/4 0, -y, 3/4
 2 a 2/m . .
 0, 0, 0 0, 0, 1/2

Symmetry of special projections

 Along [001]   2mmOrigin at 0, 0, z Along [100]   2mga' = c   Origin at x, 0, 0 Along [010]   2mma' = 1/2c   Origin at 0, y, 0

Maximal non-isotypic non-enantiomorphic subgroups

 I [2] 2cm (19) 1; 3; 6; 8 [2] m2m (2mm, 18) 1; 2; 7; 8 [2] mc21 (17) 1; 4; 6; 7 [2] 2221 (14) 1; 2; 3; 4 [2] 1121/m (12) 1; 4; 5; 8 [2] 12/c1 (2/c11, 7) 1; 2; 5; 6 [2] 2/m11 (6) 1; 3; 5; 7
 IIa none
 IIb none

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [3] mcm (c' = 3c) (22)

Minimal non-isotypic non-enantiomorphic supergroups

 I [3] 63/mmc (75)
 II [2] mmm (c' = 1/2c) (20)