pbaa mmm Orthorhombic/Rectangular No. 43 p2/b21/a2/a Patterson symmetry pmmm

Origin at -1 on b1a

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

Symmetry operations

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

Symmetry of special projections

 Along [001]   p2mg a' = b   b' = -1/2a    Origin at 0, 0, 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] pb21a (33) 1; 4; 6; 7 [2] p2aa (pb2b, 30) 1; 2; 7; 8 [2] pba2 (25) 1; 3; 6; 8 [2] p2212 (p2122, 20) 1; 2; 3; 4 [2] p121/a1 (p21/b11, 17) 1; 4; 5; 8 [2] p2/b11 (16) 1; 2; 5; 6 [2] p112/a (7) 1; 3; 5; 7
 IIa none
 IIb none

Maximal isotypic subgroups of lowest index

 IIc [3] pbaa (a' = 3a) (43); [3] pbaa (b' = 3b) (43)

Minimal non-isotypic supergroups

 I none
 II [2] cmme (48); [2] pmaa (b' = 1/2b) (38); [2] pmam (b' = 1/2b) (40)