Table of Magnetic Space Group Symbols

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Table of Magnetic Space Group Symbols

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Pn-3m' [#224.113] (Type: 3 -- Type III (translationgleiche))

[OG: Pn-3m' #224.4.1614]

Wyckoff Positions of Group 224.113 (Pn-3m')

Multiplicity

Wyckoff
letter

Coordinates

48

l

(x,y,z \| m_x,m_y,m_z)	(x+1/2,-z,y+1/2 \| -m_x,m_z,-m_y)	(x+1/2,z+1/2,-y \| -m_x,-m_z,m_y)
(z+1/2,y+1/2,-x \| -m_z,-m_y,m_x)	(-z,y+1/2,x+1/2 \| m_z,-m_y,-m_x)	(-y,x+1/2,z+1/2 \| m_y,-m_x,-m_z)
(y+1/2,-x,z+1/2 \| -m_y,m_x,-m_z)	(x,-y+1/2,-z+1/2 \| m_x,-m_y,-m_z)	(-x+1/2,y,-z+1/2 \| -m_x,m_y,-m_z)
(-x+1/2,-y+1/2,z \| -m_x,-m_y,m_z)	(y+1/2,x+1/2,-z \| -m_y,-m_x,m_z)	(-y,-x,-z \| m_y,m_x,m_z)
(-x,z+1/2,y+1/2 \| m_x,-m_z,-m_y)	(-x,-z,-y \| m_x,m_z,m_y)	(z+1/2,-y,x+1/2 \| -m_z,m_y,-m_x)
(-z,-y,-x \| m_z,m_y,m_x)	(z,x,y \| m_z,m_x,m_y)	(y,z,x \| m_y,m_z,m_x)
(-y+1/2,z,-x+1/2 \| -m_y,m_z,-m_x)	(-z+1/2,-x+1/2,y \| -m_z,-m_x,m_y)	(-y+1/2,-z+1/2,x \| -m_y,-m_z,m_x)
(z,-x+1/2,-y+1/2 \| m_z,-m_x,-m_y)	(y,-z+1/2,-x+1/2 \| m_y,-m_z,-m_x)	(-z+1/2,x,-y+1/2 \| -m_z,m_x,-m_y)
(-x,-y,-z \| m_x,m_y,m_z)	(-x+1/2,z,-y+1/2 \| -m_x,m_z,-m_y)	(-x+1/2,-z+1/2,y \| -m_x,-m_z,m_y)
(-z+1/2,-y+1/2,x \| -m_z,-m_y,m_x)	(z,-y+1/2,-x+1/2 \| m_z,-m_y,-m_x)	(y,-x+1/2,-z+1/2 \| m_y,-m_x,-m_z)
(-y+1/2,x,-z+1/2 \| -m_y,m_x,-m_z)	(-x,y+1/2,z+1/2 \| m_x,-m_y,-m_z)	(x+1/2,-y,z+1/2 \| -m_x,m_y,-m_z)
(x+1/2,y+1/2,-z \| -m_x,-m_y,m_z)	(-y+1/2,-x+1/2,z \| -m_y,-m_x,m_z)	(y,x,z \| m_y,m_x,m_z)
(x,-z+1/2,-y+1/2 \| m_x,-m_z,-m_y)	(x,z,y \| m_x,m_z,m_y)	(-z+1/2,y,-x+1/2 \| -m_z,m_y,-m_x)
(z,y,x \| m_z,m_y,m_x)	(-z,-x,-y \| m_z,m_x,m_y)	(-y,-z,-x \| m_y,m_z,m_x)
(y+1/2,-z,x+1/2 \| -m_y,m_z,-m_x)	(z+1/2,x+1/2,-y \| -m_z,-m_x,m_y)	(y+1/2,z+1/2,-x \| -m_y,-m_z,m_x)
(-z,x+1/2,y+1/2 \| m_z,-m_x,-m_y)	(-y,z+1/2,x+1/2 \| m_y,-m_z,-m_x)	(z+1/2,-x,y+1/2 \| -m_z,m_x,-m_y)

24

k

(x,x,z \| m_x,m_x,m_z)	(x+1/2,-z,x+1/2 \| -m_x,m_z,-m_x)	(x+1/2,z+1/2,-x \| -m_x,-m_z,m_x)
(z+1/2,x+1/2,-x \| -m_z,-m_x,m_x)	(-z,x+1/2,x+1/2 \| m_z,-m_x,-m_x)	(-x,x+1/2,z+1/2 \| m_x,-m_x,-m_z)
(x+1/2,-x,z+1/2 \| -m_x,m_x,-m_z)	(x,-x+1/2,-z+1/2 \| m_x,-m_x,-m_z)	(-x+1/2,x,-z+1/2 \| -m_x,m_x,-m_z)
(-x+1/2,-x+1/2,z \| -m_x,-m_x,m_z)	(x+1/2,x+1/2,-z \| -m_x,-m_x,m_z)	(-x,-x,-z \| m_x,m_x,m_z)
(-x,z+1/2,x+1/2 \| m_x,-m_z,-m_x)	(-x,-z,-x \| m_x,m_z,m_x)	(z+1/2,-x,x+1/2 \| -m_z,m_x,-m_x)
(-z,-x,-x \| m_z,m_x,m_x)	(z,x,x \| m_z,m_x,m_x)	(x,z,x \| m_x,m_z,m_x)
(-x+1/2,z,-x+1/2 \| -m_x,m_z,-m_x)	(-z+1/2,-x+1/2,x \| -m_z,-m_x,m_x)	(-x+1/2,-z+1/2,x \| -m_x,-m_z,m_x)
(z,-x+1/2,-x+1/2 \| m_z,-m_x,-m_x)	(x,-z+1/2,-x+1/2 \| m_x,-m_z,-m_x)	(-z+1/2,x,-x+1/2 \| -m_z,m_x,-m_x)

24

j

(1/2,y,-y \| m_x,m_y,m_y)	(0,y,y+1/2 \| -m_x,m_y,-m_y)	(0,-y+1/2,-y \| -m_x,-m_y,m_y)
(-y+1/2,y+1/2,1/2 \| -m_y,-m_y,m_x)	(y,y+1/2,0 \| m_y,-m_y,-m_x)	(-y,0,-y+1/2 \| m_y,-m_x,-m_y)
(y+1/2,1/2,-y+1/2 \| -m_y,m_x,-m_y)	(1/2,-y+1/2,y+1/2 \| m_x,-m_y,-m_y)	(y+1/2,0,y \| -m_y,-m_x,m_y)
(-y,1/2,y \| m_y,m_x,m_y)	(-y+1/2,-y,0 \| -m_y,m_y,-m_x)	(y,-y,1/2 \| m_y,m_y,m_x)
(1/2,-y,y \| m_x,m_y,m_y)	(0,-y,-y+1/2 \| -m_x,m_y,-m_y)	(0,y+1/2,y \| -m_x,-m_y,m_y)
(y+1/2,-y+1/2,1/2 \| -m_y,-m_y,m_x)	(-y,-y+1/2,0 \| m_y,-m_y,-m_x)	(y,0,y+1/2 \| m_y,-m_x,-m_y)
(-y+1/2,1/2,y+1/2 \| -m_y,m_x,-m_y)	(1/2,y+1/2,-y+1/2 \| m_x,-m_y,-m_y)	(-y+1/2,0,-y \| -m_y,-m_x,m_y)
(y,1/2,-y \| m_y,m_x,m_y)	(y+1/2,y,0 \| -m_y,m_y,-m_x)	(-y,y,1/2 \| m_y,m_y,m_x)

24

i

(1/2,y,y+1/2 \| m_x,m_y,-m_y)	(0,-y+1/2,y+1/2 \| -m_x,-m_y,-m_y)	(0,y,-y \| -m_x,m_y,m_y)
(y,y+1/2,1/2 \| m_y,-m_y,m_x)	(-y+1/2,y+1/2,0 \| -m_y,-m_y,-m_x)	(-y,0,y \| m_y,-m_x,m_y)
(y+1/2,1/2,y \| -m_y,m_x,m_y)	(1/2,-y+1/2,-y \| m_x,-m_y,m_y)	(y+1/2,0,-y+1/2 \| -m_y,-m_x,-m_y)
(-y,1/2,-y+1/2 \| m_y,m_x,-m_y)	(y,-y,0 \| m_y,m_y,-m_x)	(-y+1/2,-y,1/2 \| -m_y,m_y,m_x)
(1/2,-y,-y+1/2 \| m_x,m_y,-m_y)	(0,y+1/2,-y+1/2 \| -m_x,-m_y,-m_y)	(0,-y,y \| -m_x,m_y,m_y)
(-y,-y+1/2,1/2 \| m_y,-m_y,m_x)	(y+1/2,-y+1/2,0 \| -m_y,-m_y,-m_x)	(y,0,-y \| m_y,-m_x,m_y)
(-y+1/2,1/2,-y \| -m_y,m_x,m_y)	(1/2,y+1/2,y \| m_x,-m_y,m_y)	(-y+1/2,0,y+1/2 \| -m_y,-m_x,-m_y)
(y,1/2,y+1/2 \| m_y,m_x,-m_y)	(-y,y,0 \| m_y,m_y,-m_x)	(y+1/2,y,1/2 \| -m_y,m_y,m_x)

24

h

(x,1/4,3/4 \| m_x,0,0)	(x+1/2,1/4,3/4 \| -m_x,0,0)	(1/4,3/4,-x \| 0,0,m_x)
(1/4,3/4,x+1/2 \| 0,0,-m_x)	(3/4,x+1/2,1/4 \| 0,-m_x,0)	(3/4,-x,1/4 \| 0,m_x,0)
(-x+1/2,1/4,3/4 \| -m_x,0,0)	(-x,1/4,3/4 \| m_x,0,0)	(3/4,x,1/4 \| 0,m_x,0)
(1/4,3/4,x \| 0,0,m_x)	(1/4,3/4,-x+1/2 \| 0,0,-m_x)	(3/4,-x+1/2,1/4 \| 0,-m_x,0)
(-x,3/4,1/4 \| m_x,0,0)	(-x+1/2,3/4,1/4 \| -m_x,0,0)	(3/4,1/4,x \| 0,0,m_x)
(3/4,1/4,-x+1/2 \| 0,0,-m_x)	(1/4,-x+1/2,3/4 \| 0,-m_x,0)	(1/4,x,3/4 \| 0,m_x,0)
(x+1/2,3/4,1/4 \| -m_x,0,0)	(x,3/4,1/4 \| m_x,0,0)	(1/4,-x,3/4 \| 0,m_x,0)
(3/4,1/4,-x \| 0,0,m_x)	(3/4,1/4,x+1/2 \| 0,0,-m_x)	(1/4,x+1/2,3/4 \| 0,-m_x,0)

12

g

(x,1/4,1/4 \| m_x,0,0)	(x+1/2,3/4,3/4 \| -m_x,0,0)	(3/4,3/4,-x \| 0,0,m_x)
(3/4,3/4,x+1/2 \| 0,0,-m_x)	(3/4,x+1/2,3/4 \| 0,-m_x,0)	(3/4,-x,3/4 \| 0,m_x,0)
(-x+1/2,1/4,1/4 \| -m_x,0,0)	(-x,3/4,3/4 \| m_x,0,0)	(1/4,x,1/4 \| 0,m_x,0)
(1/4,1/4,x \| 0,0,m_x)	(1/4,1/4,-x+1/2 \| 0,0,-m_x)	(1/4,-x+1/2,1/4 \| 0,-m_x,0)

12

f

(1/2,1/4,3/4 \| m_x,0,0)	(0,1/4,3/4 \| -m_x,0,0)	(1/4,3/4,1/2 \| 0,0,m_x)
(1/4,3/4,0 \| 0,0,-m_x)	(3/4,0,1/4 \| 0,-m_x,0)	(3/4,1/2,1/4 \| 0,m_x,0)
(1/2,3/4,1/4 \| m_x,0,0)	(0,3/4,1/4 \| -m_x,0,0)	(3/4,1/4,1/2 \| 0,0,m_x)
(3/4,1/4,0 \| 0,0,-m_x)	(1/4,0,3/4 \| 0,-m_x,0)	(1/4,1/2,3/4 \| 0,m_x,0)

8

e

(x,x,x \| m_x,m_x,m_x)	(x+1/2,-x,x+1/2 \| -m_x,m_x,-m_x)	(x+1/2,x+1/2,-x \| -m_x,-m_x,m_x)
(-x,x+1/2,x+1/2 \| m_x,-m_x,-m_x)	(x,-x+1/2,-x+1/2 \| m_x,-m_x,-m_x)	(-x+1/2,x,-x+1/2 \| -m_x,m_x,-m_x)
(-x+1/2,-x+1/2,x \| -m_x,-m_x,m_x)	(-x,-x,-x \| m_x,m_x,m_x)

6

d

(1/4,3/4,3/4 \| 0,0,0)	(3/4,1/4,1/4 \| 0,0,0)	(1/4,1/4,3/4 \| 0,0,0)
(1/4,3/4,1/4 \| 0,0,0)	(3/4,1/4,3/4 \| 0,0,0)	(3/4,3/4,1/4 \| 0,0,0)

4

c

(1/2,1/2,1/2 \| m_x,m_x,m_x)	(0,1/2,0 \| -m_x,m_x,-m_x)	(0,0,1/2 \| -m_x,-m_x,m_x)
(1/2,0,0 \| m_x,-m_x,-m_x)

4

b

(0,0,0 \| m_x,m_x,m_x)	(1/2,0,1/2 \| -m_x,m_x,-m_x)	(1/2,1/2,0 \| -m_x,-m_x,m_x)
(0,1/2,1/2 \| m_x,-m_x,-m_x)

2

a

(1/4,1/4,1/4 | 0,0,0)

(3/4,3/4,3/4 | 0,0,0)

Site Symmetries of the Wyckoff Positions

WP	Representative	PG
2a	(1/4,1/4,1/4 \| 0,0,0)	-4'3m'
4b	(0,0,0 \| m_x,m_x,m_x)	-3
4c	(1/2,1/2,1/2 \| m_x,m_x,m_x)	-3
6d	(1/4,3/4,3/4 \| 0,0,0)	-4'2m'
8e	(x,x,x \| m_x,m_x,m_x)	3
12f	(1/2,1/4,3/4 \| m_x,0,0)	2
12g	(x,1/4,1/4 \| m_x,0,0)	2
24h	(x,1/4,3/4 \| m_x,0,0)	2
24i	(1/2,y,y+1/2 \| m_x,m_y,-m_y)	1
24j	(1/2,y,-y \| m_x,m_y,m_y)	1
24k	(x,x,z \| m_x,m_x,m_z)	1
48l	(x,y,z \| m_x,m_y,m_z)	1

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