P-4 S41 -4 Tetragonal No. 81 P-4 Patterson symmetry P4/m

Origin at -4

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

Symmetry operations

 (1)  1 (2)  2   0, 0, z (3)  -4+   0, 0, z; 0, 0, 0 (4)  -4-   0, 0, z; 0, 0, 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 h 1
 (1) x, y, z (2) -x, -y, z (3) y, -x, -z (4) -y, x, -z
no conditions
Special: as above, plus
 2 g 2 . .
 0, 1/2, z 1/2, 0, -z
hk0 : h + k = 2n
 2 f 2 . .
 1/2, 1/2, z 1/2, 1/2, -z
no extra conditions
 2 e 2 . .
 0, 0, z 0, 0, -z
no extra conditions
 1 d -4 . .
 1/2, 1/2, 1/2
no extra conditions
 1 c -4 . .
 1/2, 1/2, 0
no extra conditions
 1 b -4 . .
 0, 0, 1/2
no extra conditions
 1 a -4 . .
 0, 0, 0
no extra conditions

Symmetry of special projections

 Along [001]   p4a' = a   b' = b   Origin at 0, 0, z Along [100]   p1m1a' = b   b' = c   Origin at x, 0, 0 Along [110]   p1m1a' = 1/2(-a + b)   b' = c   Origin at x, x, 0

Maximal non-isomorphic subgroups

 I [2] P2 (3) 1; 2
 IIa none
 IIb [2] F-4 (a' = 2a, b' = 2b, c' = 2c) (I-4, 82)

Maximal isomorphic subgroups of lowest index

 IIc [2] P-4 (c' = 2c) (81); [2] C-4 (a' = 2a, b' = 2b) (P-4, 81)

Minimal non-isomorphic supergroups

 I [2] P4/m (83); [2] P42/m (84); [2] P4/n (85); [2] P42/n (86); [2] P-42m (111); [2] P-42c (112); [2] P-421m (113); [2] P-421c (114); [2] P-4m2 (115); [2] P-4c2 (116); [2] P-4b2 (117); [2] P-4n2 (118)
 II [2] I-4 (82)