cm2m m2m Orthorhombic/Rectangular No. 35 cm2m Patterson symmetry cmmm

Origin on m2m

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

Symmetry operations

For (0, 0, 0)+ set

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

For (1/21/2, 0)+ set

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

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 d 1
 (1) x, y, z (2) -x, y, -z (3) -x, y, z (4) x, y, -z
hk: h + k = 2n
h0: h = 2n
0k: k = 2n
Special: no extra conditions
 4 c . . m
 x, y, 0 -x, y, 0
 4 b m . .
 0, y, z 0, y, -z
 2 a m 2 m
 0, y, 0

Symmetry of special projections

 Along [001]   c1m1 a' = a   b' = b    Origin at 0, 0, z Along [100]   11m 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] cm11 (13) (1; 3)+ [2] c121 (c211, 10) (1; 2)+ [2] c11m (p11m, 4) (1; 4)+
 IIa [2] pb2n (34) 1; 2; (3; 4) + (1/2, 1/2, 0) [2] pm21n (32) 1; 3; (2; 4) + (1/2, 1/2, 0) [2] pb21m (29) 1; 4; (2; 3) + (1/2, 1/2, 0) [2] pm2m (27) 1; 2; 3; 4
 IIb none

Maximal isotypic subgroups of lowest index

 IIc [3] cm2m (a' = 3a) (35); [3] cm2m (b' = 3b) (35)

Minimal non-isotypic supergroups

 I [2] cmmm (47)
 II [2] pm2m (a' = 1/2a, b' = 1/2b) (27)