P41 C42 4 Tetragonal info
No. 76 P41 Patterson symmetry P4/m

symmetry group diagram

Origin on 41

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

Symmetry operations

(1)  1   (2)  2(0, 0, 1/2)   0, 0, z(3)  4+(0, 0, 1/4)   0, 0, z(4)  4-(0, 0, 3/4)   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 a 1
(1) x, y, z(2) -x, -y, z + 1/2(3) -y, x, z + 1/4(4) y, -x, z + 3/4
00l : l = 4n

Symmetry of special projections

Along [001]   p4
a' = a   b' = b   
Origin at 0, 0, z		Along [100]   p1g1
a' = b   b' = c   
Origin at x, 0, 0		Along [110]   p1g1
a' = 1/2(-a + b)   b' = c   
Origin at x, x, 0

Maximal non-isomorphic subgroups

I [2] P21 (4)1; 2
IIa none
IIbnone

Maximal isomorphic subgroups of lowest index

IIc[2] C41 (a' = 2a, b' = 2b) (P41, 76); [3] P43 (c' = 3c) (78); [5] P41 (c' = 5c) (76)

Minimal non-isomorphic supergroups

I[2] P4122 (91); [2] P41212 (92)
II[2] I41 (80); [2] P42 (c' = 1/2c) (77)








































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