p21212 222 Orthorhombic/Rectangular No. 21 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

Symmetry operations

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

Generators selected (1); t(1, 0, 0); t(0, 1, 0); (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
h0: h = 2n
0k: k = 2n
Special: as above, plus
 2 b . . 2
 0, 1/2, z 1/2, 0, -z
hk: h + k = 2n
 2 a . . 2
 0, 0, z 1/2, 1/2, -z
hk: h + k = 2n

Symmetry of special projections

 Along [001]   p2gg a' = a   b' = b    Origin at 0, 0, z Along [100]   2mg a' = b    Origin at x, 1/4, 0 Along [010]   2mg a' = a    Origin at 1/4, y, 0

Maximal non-isotypic subgroups

 I [2] p1211 (p2111, 9) 1; 3 [2] p2111 (9) 1; 4 [2] p112 (3) 1; 2
 IIa none
 IIb none

Maximal isotypic subgroups of lowest index

 IIc [3] p21212 (a' = 3a or b' = 3b) (21)

Minimal non-isotypic supergroups

 I [2] pbam (44); [2] pmmn (46); [2] p4212 (54); [2] p-421m (58)
 II [2] c222 (22); [2] p2212 (a' = 1/2a) (p2122, 20)