4mm 4mm Tetragonal No. 34 4mm Patterson symmetry 4/mmm

Origin on 4mm

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

Symmetry operations

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 8 d 1
 (1) x, y, z (2) -x, -y, z (3) -y, x, z (4) y, -x, z (5) x, -y, z (6) -x, y, z (7) -y, -x, z (8) y, x, z
no conditions
Special: no extra conditions
 4 c . m .
 x, 0, z -x, 0, z 0, x, z 0, -x, z
 4 b . . m
 x, x, z -x, -x, z -x, x, z x, -x, z
 1 a 4 m m
 0, 0, z

Symmetry of special projections

 Along [001]   4mmOrigin at 0, 0, z Along [100]   11ma' = c   Origin at x, 0, 0 Along [110]   11ma' = c   Origin at x, x, 0

Maximal non-isotypic non-enantiomorphic subgroups

 I [2] 411 (4, 23) 1; 2; 3; 4 [2] 2m1 (mm2, 15) 1; 2; 5; 6 [2] 21m (mm2, 15) 1; 2; 7; 8
 IIa none
 IIb [2] 4cc (c' = 2c) (36); [2] 42mc (c' = 2c) (42cm, 35); [2] 42cm (c' = 2c) (35)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [2] 4mm (c' = 2c) (34)

Minimal non-isotypic non-enantiomorphic supergroups

 I [2] 4/mmm (39)
 II none