pban mmm Orthorhombic/Rectangular No. 39 p2/b2/a2/n Patterson symmetry pmmm

Origin at -1 at ban, at -1/4, -1/4, 0 from 222

 Asymmetric unit 0 ≤ x ≤ 1/4; 0 ≤ y ≤ 1; 0 ≤ z

Symmetry operations

 (1)  1 (2)  2   1/4, 1/4, z (3)  2   1/4, y, 0 (4)  2   x, 1/4, 0 (5)  -1   0, 0, 0 (6)  n(1/2, 1/2, 0)   x, y, 0 (7)  a   x, 0, z (8)  b   0, y, z

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 8 h 1
 (1) x, y, z (2) -x + 1/2, -y + 1/2, z (3) -x + 1/2, y, -z (4) x, -y + 1/2, -z (5) -x, -y, -z (6) x + 1/2, y + 1/2, -z (7) x + 1/2, -y, z (8) -x, y + 1/2, z
hk: h + k = 2n
h0: h = 2n
0k: k = 2n
Special: as above, plus
 4 g . . 2
 1/4, 3/4, z 1/4, 3/4, -z 3/4, 1/4, -z 3/4, 1/4, z
no extra conditions
 4 f . . 2
 1/4, 1/4, z 1/4, 1/4, -z 3/4, 3/4, -z 3/4, 3/4, z
no extra conditions
 4 e . 2 .
 1/4, y, 0 1/4, -y + 1/2, 0 3/4, -y, 0 3/4, y + 1/2, 0
no extra conditions
 4 d 2 . .
 x, 1/4, 0 -x + 1/2, 1/4, 0 -x, 3/4, 0 x + 1/2, 3/4, 0
no extra conditions
 4 c -1
 0, 0, 0 1/2, 1/2, 0 1/2, 0, 0 0, 1/2, 0
hk: hk = 2n
 2 b 2 2 2
 3/4, 1/4, 0 1/4, 3/4, 0
no extra conditions
 2 a 2 2 2
 1/4, 1/4, 0 3/4, 3/4, 0
no extra conditions

Symmetry of special projections

 Along [001]   c2mm a' = a   b' = b    Origin at 1/4, 1/4, z Along [100]   2mm a' = 1/2b    Origin at x, 0, 0 Along [010]   2mm a' = 1/2a    Origin at 0, y, 0

Maximal non-isotypic subgroups

 I [2] pb2n (34) 1; 3; 6; 8 [2] p2an (pb2n, 34) 1; 4; 6; 7 [2] pba2 (25) 1; 2; 7; 8 [2] p222 (19) 1; 2; 3; 4 [2] p12/a1 (p2/b11, 16) 1; 3; 5; 7 [2] p2/b11 (16) 1; 4; 5; 8 [2] p112/n (p112/a, 7) 1; 2; 5; 6
 IIa none
 IIb none

Maximal isotypic subgroups of lowest index

 IIc [3] pban (a' = 3a or b' = 3b) (39)

Minimal non-isotypic supergroups

 I [2] p4/nbm (62)
 II [2] cmmm (47); [2] pmaa (b' = 1/2b) (38)