c2mm 2mm Rectangular No. 9 c2mm Patterson symmetry c2mm

Origin at 2 m m

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

Symmetry operations

For (0, 0)+ set

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

For (1/21/2)+ set

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

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

Maximal non-isomorphic subgroups

 I [2] c1m1 (cm, 5) (1; 3)+ [2] c11m (cm, 5) (1; 4)+ [2] c211 (p2, 2) (1; 2)+
 IIa [2] p2gg (8) 1; 2; (3; 4) + (1/2, 1/2) [2] p2gm (p2mg, 7) 1; 4; (2; 3) + (1/2, 1/2) [2] p2mg (7) 1; 3; (2; 4) + (1/2, 1/2) [2] p2mm (6) 1; 2; 3; 4
 IIb none

Maximal isomorphic subgroups of lowest index

 IIc [3] c2mm (a' = 3a or b' = 3b) (9)

Minimal non-isomorphic supergroups

 I [2] p4mm (11); [2] p4gm (12); [3] p6mm (17)
 II [2] p2mm(a' = 1/2a, b' = 1/2b) (6)