Pmn21 C2v7 mm2 Orthorhombic No. 31 Pmn21 Patterson symmetry Pmmm

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]   p2mga' = a   b' = b   Origin at 1/4, 0, z Along [100]   p1g1a' = b   b' = c   Origin at x, 0, 0 Along [010]   c11ma' = 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)