P42 C43 4 Tetragonal info
No. 77 P42 Patterson symmetry P4/m

symmetry group diagram

Origin on 2 on 42

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, 1/2)   0, 0, z(4)  4-(0, 0, 1/2)   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 + 1/2(4) y, -x, z + 1/2
00l : l = 2n
    Special: as above, plus
2 c  2 . . 
0, 1/2, z 1/2, 0, z + 1/2
hkl : h + k + l = 2n
2 b  2 . . 
1/2, 1/2, z 1/2, 1/2, z + 1/2
hkl : l = 2n
2 a  2 . . 
0, 0, z 0, 0, z + 1/2
hkl : l = 2n

Symmetry of special projections

Along [001]   p4
a' = a   b' = b   
Origin at 0, 0, z		Along [100]   p1m1
a' = b   b' = c   
Origin at x, 0, 0		Along [110]   p1m1
a' = 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] P43 (c' = 2c) (78); [2] P41 (c' = 2c) (76); [2] F41 (a' = 2a, b' = 2b, c' = 2c) (I41, 80)

Maximal isomorphic subgroups of lowest index

IIc[2] C42 (a' = 2a, b' = 2b) (P42, 77); [3] P42 (c' = 3c) (77)

Minimal non-isomorphic supergroups

I[2] P42/m (84); [2] P42/n (86); [2] P4222 (93); [2] P42212 (94); [2] P42cm (101); [2] P42nm (102); [2] P42mc (105); [2] P42bc (106)
II[2] I4 (79); [2] P4 (c' = 1/2c) (75)








































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