P212121 D24 222 Orthorhombic No. 19 P212121 Patterson symmetry Pmmm

Origin at midpoint of three non-intersecting pairs of parallel 21 axes

 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)  2(0, 1/2, 0)   0, y, 1/4 (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 a 1
 (1) x, y, z (2) -x + 1/2, -y, z + 1/2 (3) -x, y + 1/2, -z + 1/2 (4) x + 1/2, -y + 1/2, -z
h00 : h = 2n
0k0 : k = 2n
00l : l = 2n

Symmetry of special projections

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

Maximal non-isomorphic subgroups

 I [2] P1121 (P21, 4) 1; 2 [2] P1211 (P21, 4) 1; 3 [2] P2111 (P21, 4) 1; 4
 IIa none
 IIb none

Maximal isomorphic subgroups of lowest index

 IIc [3] P212121 (a' = 3a or b' = 3b or c' = 3c) (19)

Minimal non-isomorphic supergroups

 I [2] Pbca (61); [2] Pnma (62); [2] P41212 (92); [2] P43212 (96); [3] P213 (198)
 II [2] A2122 (C2221, 20); [2] B2212 (C2221, 20); [2] C2221 (20); [2] I212121 (24); [2] P22121 (a' = 1/2a) (P21212, 18); [2] P21221 (b' = 1/2b) (P21212, 18); [2] P21212 (c' = 1/2c) (18)