pba2 mm2 Orthorhombic/Rectangular No. 25 pba2 Patterson symmetry pmmm

Origin on 112

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

Symmetry operations

 (1)  1       (1 | 0, 0, 0) (2)  2   0, 0, z       (2z | 0, 0, 0) (3)  a   x, 1/4, z       (my | 1/2, 1/2, 0) (4)  b   1/4, y, z       (mx | 1/2, 1/2, 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 c 1
 (1) x, y, z (2) -x, -y, z (3) x + 1/2, -y + 1/2, z (4) -x + 1/2, y + 1/2, z
h0: h = 2n
0k: k = 2n
Special: as above, plus
 2 b . . 2
 0, 1/2, z 1/2, 0, z
hk: h + k = 2n
 2 a . . 2
 0, 0, z 1/2, 1/2, z
hk: h + k = 2n

Symmetry of special projections

 Along [001]   p2gg a' = a   b' = b    Origin at 0, 0, z Along [100]   1m1 a' = 1/2b    Origin at x, 0, 0 Along [010]   1m1 a' = 1/2a    Origin at 0, y, 0

Maximal non-isotypic subgroups

 I [2] p1a1 (pb11, 12) 1; 3 [2] pb11 (12) 1; 4 [2] p112 (3) 1; 2
 IIa none
 IIb none

Maximal isotypic subgroups of lowest index

 IIc [3] pba2 (a' = 3a or b' = 3b) (25)

Minimal non-isotypic supergroups

 I [2] pban (39); [2] pbaa (43); [2] pbam (44); [2] p4bm (56); [2] p-4b2 (60)
 II [2] cmm2 (26); [2] pma2 (b' = 1/2b) (24)