pmm2 mm2 Orthorhombic/Rectangular No. 23 pmm2 Patterson symmetry pmmm

Origin on mm2

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

Symmetry operations

 (1)  1 (2)  2   0, 0, z (3)  m   x, 0, z (4)  m   0, y, z

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 4 i 1
 (1) x, y, z (2) -x, -y, z (3) x, -y, z (4) -x, y, z
no conditions
Special: no extra conditions
 2 h m . .
 1/2, y, z 1/2, -y, z
 2 g m . .
 0, y, z 0, -y, z
 2 f . m .
 x, 1/2, z -x, 1/2, z
 2 e . m .
 x, 0, z -x, 0, z
 1 d m m 2
 1/2, 1/2, z
 1 c m m 2
 1/2, 0, z
 1 b m m 2
 0, 1/2, z
 1 a m m 2
 0, 0, z

Symmetry of special projections

 Along [001]   p2mm a' = a   b' = b    Origin at 0, 0, z Along [100]   1m1 a' = b    Origin at x, 0, 0 Along [010]   1m1 a' = a    Origin at 0, y, 0

Maximal non-isotypic subgroups

 I [2] p1m1 (pm11, 11) 1; 3 [2] pm11 (11) 1; 4 [2] p112 (3) 1; 2
 IIa none
 IIb [2] cmm2 (a' = 2a, b' = 2b) (26); [2] pma2 (a' = 2a) (24); [2] pbm2 (b' = 2b) (pma2, 24)

Maximal isotypic subgroups of lowest index

 IIc [2] pmm2 (a' = 2a or b' = 2b) (23)

Minimal non-isotypic supergroups

 I [2] pmmm (37); [2] pmma (41); [2] pmmn (46); [2] p4mm (55); [2] p-4m2 (59)
 II [2] cmm2 (26)