p2gg 2mm Rectangularinfo
No. 8 p2gg Patterson symmetry p2mm

symmetry group diagram

Origin at 2

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

Symmetry operations

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry		 Coordinates Reflection conditions
 General:
4 c 1
(1) x, y(2) -x, -y(3) -x + 1/2, y + 1/2(4) x + 1/2, -y + 1/2
h0 : h = 2n
0k : k = 2n
    Special: as above, plus
2 b  2 . . 
1/2, 0 0, 1/2
hk : h + k = 2n
2 a  2 . . 
0, 0 1/2, 1/2
hk : h + k = 2n

Maximal non-isomorphic subgroups

I[2] p1g1 (pg, 4)1; 3
 [2] p11g (pg, 4)1; 4
 [2] p211 (p2, 2)1; 2
IIa none
IIbnone

Maximal isomorphic subgroups of lowest index

IIc[3] p2gg (a' = 3a or b' = 3b) (8)

Minimal non-isomorphic supergroups

I[2] p4gm (12)
II[2] c2mm (9); [2] p2mg(a' = 1/2 a) (7); [2] p2gm(b' = 1/2 b) (p2mg, 7)








































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