P4 C41 4 Tetragonal No. 75 P4 Patterson symmetry P4/m

Origin on 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 (4)  4-   0, 0, z

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 d 1
 (1) x, y, z (2) -x, -y, z (3) -y, x, z (4) y, -x, z
no conditions
Special: as above, plus
 2 c 2 . .
 0, 1/2, z 1/2, 0, z
hkl : h + k = 2n
 1 b 4 . .
 1/2, 1/2, z
no extra conditions
 1 a 4 . .
 0, 0, z
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] P42 (c' = 2c) (77); [2] F4 (a' = 2a, b' = 2b, c' = 2c) (I4, 79)

Maximal isomorphic subgroups of lowest index

 IIc [2] P4 (c' = 2c) (75); [2] C4 (a' = 2a, b' = 2b) (P4, 75)

Minimal non-isomorphic supergroups

 I [2] P4/m (83); [2] P4/n (85); [2] P422 (89); [2] P4212 (90); [2] P4mm (99); [2] P4bm (100); [2] P4cc (103); [2] P4nc (104)
 II [2] I4 (79)