cmm2 mm2 Orthorhombic/Rectangular No. 26 cmm2 Patterson symmetry cmmm

Origin on mm2

 Asymmetric unit 0 ≤ x ≤ 1/4; 0 ≤ y ≤ 1/2

Symmetry operations

For (0, 0, 0)+ set

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

For (1/21/2, 0)+ set

 (1)  t(1/2, 1/2, 0) (2)  2   1/4, 1/4, z (3)  a   x, 1/4, z (4)  b   1/4, y, z

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(1/21/2, 0); (2); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

(0, 0, 0)+  (1/21/2, 0)+   General:
 8 f 1
 (1) x, y, z (2) -x, -y, z (3) x, -y, z (4) -x, y, z
hk: h + k = 2n
0k: k = 2n
h0: h = 2n
Special: as above, plus
 4 e m . .
 0, y, z 0, -y, z
no extra conditions
 4 d . m .
 x, 0, z -x, 0, z
no extra conditions
 4 c . . 2
 1/4, 1/4, z 1/4, 3/4, z
hk: h = 2n
 2 b m m 2
 0, 1/2, z
no extra conditions
 2 a m m 2
 0, 0, z
no extra conditions

Symmetry of special projections

 Along [001]   c2mm 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] c1m1 (cm11, 13) (1; 3)+ [2] cm11 (13) (1; 4)+ [2] c112 (p112, 3) (1; 2)+
 IIa [2] pba2 (25) 1; 2; (3; 4) + (1/2, 1/2, 0) [2] pbm2 (pma2, 24) 1; 3; (2; 4) + (1/2, 1/2, 0) [2] pma2 (24) 1; 4; (2; 3) + (1/2, 1/2, 0) [2] pmm2 (23) 1; 2; 3; 4
 IIb none

Maximal isotypic subgroups of lowest index

 IIc [3] cmm2 (a' = 3a or b' = 3b) (26)

Minimal non-isotypic supergroups

 I [2] cmmm (47); [2] cmme (48); [2] p4mm (55); [2] p4bm (56); [2] p-42m (57); [2] p-421m (58); [3] p6mm (77)
 II [2] pmm2 (a' = 1/2a, b' = 1/2b) (23)