4322 422 Tetragonal No. 33 4322 Patterson symmetry 4/mmm

Origin on 2[100] at 43(2,1)1

 Asymmetric unit 0 ≤ z ≤ 1/8

Symmetry operations

 (1)  1 (2)  2(1/2)   0, 0, z (3)  4+(3/4)   0, 0, z (4)  4-(1/4)   0, 0, z (5)  2   x, 0, 0 (6)  2   0, y, 1/4 (7)  2   x, x, 3/8 (8)  2   x, -x, 1/8

Generators selected (1); t(0, 0, 1); (2); (3); (5)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 8 c 1
 (1) x, y, z (2) -x, -y, z + 1/2 (3) -y, x, z + 3/4 (4) y, -x, z + 1/4 (5) x, -y, -z (6) -x, y, -z + 1/2 (7) y, x, -z + 3/4 (8) -y, -x, -z + 1/4
l: l = 4n
Special: no extra conditions
 4 b . . 2
 x, x, 7/8 -x, -x, 3/8 -x, x, 5/8 x, -x, 1/8
 4 a . 2 .
 x, 0, 0 -x, 0, 1/2 0, x, 3/4 0, -x, 1/4

Symmetry of special projections

 Along [001]   4mmOrigin at 0, 0, z Along [100]   2mga' = c   Origin at x, 0, 0 Along [110]   2mga' = c   Origin at x, x, 3/8

Maximal non-isotypic non-enantiomorphic subgroups

 I [2] 4311 (43, 26) 1; 2; 3; 4 [2] 2121 (2221, 14) 1; 2; 5; 6 [2] 2112 (2221, 14) 1; 2; 7; 8
 IIa none
 IIb none

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [3] 4122 (c' = 3c) (31); [5] 4322 (c' = 5c) (33)

Minimal non-isotypic non-enantiomorphic supergroups

 I none
 II [2] 4222 (c' = 1/2c) (32)