P21212 D23 222 Orthorhombic No. 18 P21212 Patterson symmetry Pmmm

Origin at intersection of 2 with perpendicular plane containing 21 axes

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

Symmetry operations

 (1)  1 (2)  2   0, 0, 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(0, 0, 1); (2); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 4 c 1
 (1) x, y, z (2) -x, -y, z (3) -x + 1/2, y + 1/2, -z (4) x + 1/2, -y + 1/2, -z
h00 : h = 2n
0k0 : k = 2n
Special: as above, plus
 2 b . . 2
 0, 1/2, z 1/2, 0, -z
hk0 : h + k = 2n
 2 a . . 2
 0, 0, z 1/2, 1/2, -z
hk0 : h + k = 2n

Symmetry of special projections

 Along [001]   p2gga' = a   b' = b   Origin at 0, 0, z Along [100]   p2mga' = b   b' = c   Origin at x, 1/4, 0 Along [010]   p2gma' = c   b' = a   Origin at 1/4, y, 0

Maximal non-isomorphic subgroups

 I [2] P1211 (P21, 4) 1; 3 [2] P2111 (P21, 4) 1; 4 [2] P112 (P2, 3) 1; 2
 IIa none
 IIb [2] P212121 (c' = 2c) (19)

Maximal isomorphic subgroups of lowest index

 IIc [2] P21212 (c' = 2c) (18); [3] P21212 (a' = 3a or b' = 3b) (18)

Minimal non-isomorphic supergroups

 I [2] Pbam (55); [2] Pccn (56); [2] Pbcm (57); [2] Pnnm (58); [2] Pmmn (59); [2] Pbcn (60); [2] P4212 (90); [2] P42212 (94); [2] P-421m (113); [2] P-421c (114)
 II [2] A2122 (C2221, 20); [2] B2212 (C2221, 20); [2] C222 (21); [2] I222 (23); [2] P2212 (a' = 1/2a) (P2221, 17); [2] P2122 (b' = 1/2b) (P2221, 17)