c222 222 Orthorhombic/Rectangular No. 22 c222 Patterson symmetry cmmm

Origin at 222

 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)  2   0, y, 0 (4)  2   x, 0, 0

For (1/21/2, 0)+ set

 (1)  t(1/2, 1/2, 0) (2)  2   1/4, 1/4, z (3)  2(0, 1/2, 0)   1/4, y, 0 (4)  2(1/2, 0, 0)   x, 1/4, 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 h 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 g . . 2
 1/4, 1/4, z 3/4, 1/4, -z
hk: h = 2n
 4 f . . 2
 0, 1/2, z 0, 1/2, -z
no extra conditions
 4 e . . 2
 0, 0, z 0, 0, -z
no extra conditions
 4 d . 2 .
 0, y, 0 0, -y, 0
no extra conditions
 4 c 2 . .
 x, 0, 0 -x, 0, 0
no extra conditions
 2 b 2 2 2
 0, 1/2, 0
no extra conditions
 2 a 2 2 2
 0, 0, 0
no extra conditions

Symmetry of special projections

 Along [001]   c2mm a' = a   b' = b    Origin at 0, 0, z Along [100]   2mm 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] c121 (c211, 10) (1; 3)+ [2] c211 (10) (1; 4)+ [2] c112 (p112, 3) (1; 2)+
 IIa [2] p21212 (21) 1; 2; (3; 4) + (1/2, 1/2, 0) [2] p2122 (20) 1; 3; (2; 4) + (1/2, 1/2, 0) [2] p2212 (p2122, 20) 1; 4; (2; 3) + (1/2, 1/2, 0) [2] p222 (19) 1; 2; 3; 4
 IIb none

Maximal isotypic subgroups of lowest index

 IIc [3] c222 (a' = 3a or b' = 3b) (22)

Minimal non-isotypic supergroups

 I [2] cmmm (47); [2] cmme (48); [2] p422 (53); [2] p4212 (54); [2] p-4m2 (59); [2] p-4b2 (60); [3] p622 (76)
 II [2] p222 (a' = 1/2a, b' = 1/2b) (19)