Pmn21 C2v7 mm2 Orthorhombic info
No. 31 Pmn21 Patterson symmetry Pmmm

symmetry group diagram

Origin on m n 1

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

Symmetry operations

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry		 Coordinates Reflection conditions
 General:
4 b 1
(1) x, y, z(2) -x + 1/2, -y, z + 1/2(3) x + 1/2, -y, z + 1/2(4) -x, y, z
h0l : h + l = 2n
h00 : h = 2n
00l : l = 2n
    Special: as above, plus
2 a  m . . 
0, y, z 1/2, -y, z + 1/2
no extra conditions

Symmetry of special projections

Along [001]   p2mg
a' = a   b' = b   
Origin at 1/4, 0, z		Along [100]   p1g1
a' = b   b' = c   
Origin at x, 0, 0		Along [010]   c11m
a' = c   b' = a   
Origin at 0, y, 0

Maximal non-isomorphic subgroups

I [2] P1n1 (Pc, 7)1; 3
  [2] Pm11 (Pm, 6)1; 4
  [2] P1121 (P21, 4)1; 2
IIa none
IIb[2] Pbn21 (b' = 2b) (Pna21, 33)

Maximal isomorphic subgroups of lowest index

IIc[2] Pmn21 (b' = 2b) (31); [3] Pmn21 (a' = 3a) (31); [3] Pmn21 (c' = 3c) (31)

Minimal non-isomorphic supergroups

I[2] Pmna (53); [2] Pnnm (58); [2] Pmmn (59); [2] Pnma (62)
II[2] Cmc21 (36); [2] Bmm2 (Amm2, 38); [2] Ama2 (40); [2] Imm2 (44); [2] Pmc21 (a' = 1/2a) (26); [2] Pma2 (c' = 1/2c) (28)








































to end of page
to top of page