p2122 222 Orthorhombic/Rectangular No. 20 p2122 Patterson symmetry pmmm

Origin at 2112

 Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/2; 0 ≤ z

Symmetry operations

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 4 d 1
 (1) x, y, z (2) x + 1/2, -y, -z (3) -x + 1/2, y, -z (4) -x, -y, z
h0: h = 2n
Special: as above, plus
 2 c . 2 .
 1/4, y, 0 3/4, -y, 0
no extra conditions
 2 b . . 2
 0, 1/2, z 1/2, 1/2, -z
hk: h = 2n
 2 a . . 2
 0, 0, z 1/2, 0, -z
hk: h = 2n

Symmetry of special projections

 Along [001]   p2mg a' = a   b' = b    Origin at 0, 0, z Along [100]   2mm a' = b    Origin at x, 0, 0 Along [010]   2mg a' = a    Origin at 1/4, y, 0

Maximal non-isotypic subgroups

 I [2] p2111 (9) 1; 2 [2] p121 (p211, 8) 1; 3 [2] p112 (3) 1; 4
 IIa none
 IIb [2] p21212 (b' = 2b) (21)

Maximal isotypic subgroups of lowest index

 IIc [2] p2122 (b' = 2b) (20); [3] p2122 (a' = 3a) (20)

Minimal non-isotypic supergroups

 I [2] pmam (40); [2] pmma (41); [2] pman (42); [2] pbaa (43); [2] pbma (45)
 II [2] c222 (22); [2] p222 (a' = 1/2a) (19)