Wyckoff Positions of Space Groups

Wyckoff Positions of Group 222 (P n -3 n) [origin choice 2]

Multiplicity

Wyckoff
letter

Site
symmetry

Coordinates

48

i

1

(x, y, z)	( - x + 1/2, - y + 1/2, z)	( - x + 1/2, y, - z + 1/2)	(x, - y + 1/2, - z + 1/2)
(z, x, y)	(z, - x + 1/2, - y + 1/2)	( - z + 1/2, - x + 1/2, y)	( - z + 1/2, x, - y + 1/2)
(y, z, x)	( - y + 1/2, z, - x + 1/2)	(y, - z + 1/2, - x + 1/2)	( - y + 1/2, - z + 1/2, x)
(y, x, - z + 1/2)	( - y + 1/2, - x + 1/2, - z + 1/2)	(y, - x + 1/2, z)	( - y + 1/2, x, z)
(x, z, - y + 1/2)	( - x + 1/2, z, y)	( - x + 1/2, - z + 1/2, - y + 1/2)	(x, - z + 1/2, y)
(z, y, - x + 1/2)	(z, - y + 1/2, x)	( - z + 1/2, y, x)	( - z + 1/2, - y + 1/2, - x + 1/2)
( - x, - y, - z)	(x + 1/2, y + 1/2, - z)	(x + 1/2, - y, z + 1/2)	( - x, y + 1/2, z + 1/2)
( - z, - x, - y)	( - z, x + 1/2, y + 1/2)	(z + 1/2, x + 1/2, - y)	(z + 1/2, - x, y + 1/2)
( - y, - z, - x)	(y + 1/2, - z, x + 1/2)	( - y, z + 1/2, x + 1/2)	(y + 1/2, z + 1/2, - x)
( - y, - x, z + 1/2)	(y + 1/2, x + 1/2, z + 1/2)	( - y, x + 1/2, - z)	(y + 1/2, - x, - z)
( - x, - z, y + 1/2)	(x + 1/2, - z, - y)	(x + 1/2, z + 1/2, y + 1/2)	( - x, z + 1/2, - y)
( - z, - y, x + 1/2)	( - z, y + 1/2, - x)	(z + 1/2, - y, - x)	(z + 1/2, y + 1/2, x + 1/2)

24

h

..2

(1/4, y, y)	(1/4, - y + 1/2, y)	(1/4, y, - y + 1/2)	(1/4, - y + 1/2, - y + 1/2)
(y, 1/4, y)	(y, 1/4, - y + 1/2)	( - y + 1/2, 1/4, y)	( - y + 1/2, 1/4, - y + 1/2)
(y, y, 1/4)	( - y + 1/2, y, 1/4)	(y, - y + 1/2, 1/4)	( - y + 1/2, - y + 1/2, 1/4)
(3/4, - y, - y)	(3/4, y + 1/2, - y)	(3/4, - y, y + 1/2)	(3/4, y + 1/2, y + 1/2)
( - y, 3/4, - y)	( - y, 3/4, y + 1/2)	(y + 1/2, 3/4, - y)	(y + 1/2, 3/4, y + 1/2)
( - y, - y, 3/4)	(y + 1/2, - y, 3/4)	( - y, y + 1/2, 3/4)	(y + 1/2, y + 1/2, 3/4)

24

g

2..

(x, 3/4, 1/4)	( - x + 1/2, 3/4, 1/4)	(1/4, x, 3/4)	(1/4, - x + 1/2, 3/4)
(3/4, 1/4, x)	(3/4, 1/4, - x + 1/2)	(3/4, x, 1/4)	(3/4, - x + 1/2, 1/4)
(x, 1/4, 3/4)	( - x + 1/2, 1/4, 3/4)	(1/4, 3/4, - x + 1/2)	(1/4, 3/4, x)
( - x, 1/4, 3/4)	(x + 1/2, 1/4, 3/4)	(3/4, - x, 1/4)	(3/4, x + 1/2, 1/4)
(1/4, 3/4, - x)	(1/4, 3/4, x + 1/2)	(1/4, - x, 3/4)	(1/4, x + 1/2, 3/4)
( - x, 3/4, 1/4)	(x + 1/2, 3/4, 1/4)	(3/4, 1/4, x + 1/2)	(3/4, 1/4, - x)

16

f

.3.

(x, x, x)	( - x + 1/2, - x + 1/2, x)	( - x + 1/2, x, - x + 1/2)	(x, - x + 1/2, - x + 1/2)
(x, x, - x + 1/2)	( - x + 1/2, - x + 1/2, - x + 1/2)	(x, - x + 1/2, x)	( - x + 1/2, x, x)
( - x, - x, - x)	(x + 1/2, x + 1/2, - x)	(x + 1/2, - x, x + 1/2)	( - x, x + 1/2, x + 1/2)
( - x, - x, x + 1/2)	(x + 1/2, x + 1/2, x + 1/2)	( - x, x + 1/2, - x)	(x + 1/2, - x, - x)

12

e

4..

(x, 1/4, 1/4)	( - x + 1/2, 1/4, 1/4)	(1/4, x, 1/4)	(1/4, - x + 1/2, 1/4)
(1/4, 1/4, x)	(1/4, 1/4, - x + 1/2)	( - x, 3/4, 3/4)	(x + 1/2, 3/4, 3/4)
(3/4, - x, 3/4)	(3/4, x + 1/2, 3/4)	(3/4, 3/4, - x)	(3/4, 3/4, x + 1/2)

12

d

-4..

(0, 3/4, 1/4)	(1/2, 3/4, 1/4)	(1/4, 0, 3/4)	(1/4, 1/2, 3/4)
(3/4, 1/4, 0)	(3/4, 1/4, 1/2)	(3/4, 0, 1/4)	(3/4, 1/2, 1/4)
(0, 1/4, 3/4)	(1/2, 1/4, 3/4)	(1/4, 3/4, 1/2)	(1/4, 3/4, 0)

8

c

.-3.

(0, 0, 0)	(1/2, 1/2, 0)	(1/2, 0, 1/2)	(0, 1/2, 1/2)
(0, 0, 1/2)	(1/2, 1/2, 1/2)	(0, 1/2, 0)	(1/2, 0, 0)

6

b

42. 2

(3/4, 1/4, 1/4)	(1/4, 3/4, 1/4)	(1/4, 1/4, 3/4)	(1/4, 3/4, 3/4)
(3/4, 1/4, 3/4)	(3/4, 3/4, 1/4)

2

a

432

(1/4, 1/4, 1/4)

(3/4, 3/4, 3/4)

If you want to see the Wyckoff position in other setting, click here

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