Table of Magnetic Space Group Symbols

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Table of Magnetic Space Group Symbols

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Fm'-3'm' [#225.120] (Type: 3 -- Type III (translationgleiche))

[OG: Fm'-3'm' #225.5.1622]

Wyckoff Positions of Group 225.120 (Fm'-3'm')

Multiplicity

Wyckoff
letter

Coordinates

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

192

l

(x,y,z \| m_x,m_y,m_z)	(x,-z,y \| m_x,-m_z,m_y)	(x,z,-y \| m_x,m_z,-m_y)
(z,y,-x \| m_z,m_y,-m_x)	(-z,y,x \| -m_z,m_y,m_x)	(-y,x,z \| -m_y,m_x,m_z)
(y,-x,z \| m_y,-m_x,m_z)	(x,-y,-z \| m_x,-m_y,-m_z)	(-x,y,-z \| -m_x,m_y,-m_z)
(-x,-y,z \| -m_x,-m_y,m_z)	(y,x,-z \| m_y,m_x,-m_z)	(-y,-x,-z \| -m_y,-m_x,-m_z)
(-x,z,y \| -m_x,m_z,m_y)	(-x,-z,-y \| -m_x,-m_z,-m_y)	(z,-y,x \| 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,z,-x \| -m_y,m_z,-m_x)	(-z,-x,y \| -m_z,-m_x,m_y)	(-y,-z,x \| -m_y,-m_z,m_x)
(z,-x,-y \| m_z,-m_x,-m_y)	(y,-z,-x \| m_y,-m_z,-m_x)	(-z,x,-y \| -m_z,m_x,-m_y)
(-x,-y,-z \| -m_x,-m_y,-m_z)	(-x,z,-y \| -m_x,m_z,-m_y)	(-x,-z,y \| -m_x,-m_z,m_y)
(-z,-y,x \| -m_z,-m_y,m_x)	(z,-y,-x \| m_z,-m_y,-m_x)	(y,-x,-z \| m_y,-m_x,-m_z)
(-y,x,-z \| -m_y,m_x,-m_z)	(-x,y,z \| -m_x,m_y,m_z)	(x,-y,z \| m_x,-m_y,m_z)
(x,y,-z \| m_x,m_y,-m_z)	(-y,-x,z \| -m_y,-m_x,m_z)	(y,x,z \| m_y,m_x,m_z)
(x,-z,-y \| m_x,-m_z,-m_y)	(x,z,y \| m_x,m_z,m_y)	(-z,y,-x \| -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,-z,x \| m_y,-m_z,m_x)	(z,x,-y \| m_z,m_x,-m_y)	(y,z,-x \| m_y,m_z,-m_x)
(-z,x,y \| -m_z,m_x,m_y)	(-y,z,x \| -m_y,m_z,m_x)	(z,-x,y \| m_z,-m_x,m_y)

96

k

(x,x,z \| m_x,m_x,m_z)	(x,-z,x \| m_x,-m_z,m_x)	(x,z,-x \| m_x,m_z,-m_x)
(z,x,-x \| m_z,m_x,-m_x)	(-z,x,x \| -m_z,m_x,m_x)	(-x,x,z \| -m_x,m_x,m_z)
(x,-x,z \| m_x,-m_x,m_z)	(x,-x,-z \| m_x,-m_x,-m_z)	(-x,x,-z \| -m_x,m_x,-m_z)
(-x,-x,z \| -m_x,-m_x,m_z)	(x,x,-z \| m_x,m_x,-m_z)	(-x,-x,-z \| -m_x,-m_x,-m_z)
(-x,z,x \| -m_x,m_z,m_x)	(-x,-z,-x \| -m_x,-m_z,-m_x)	(z,-x,x \| 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,z,-x \| -m_x,m_z,-m_x)	(-z,-x,x \| -m_z,-m_x,m_x)	(-x,-z,x \| -m_x,-m_z,m_x)
(z,-x,-x \| m_z,-m_x,-m_x)	(x,-z,-x \| m_x,-m_z,-m_x)	(-z,x,-x \| -m_z,m_x,-m_x)

96

j

(0,y,z \| 0,m_y,m_z)	(0,-z,y \| 0,-m_z,m_y)	(0,z,-y \| 0,m_z,-m_y)
(z,y,0 \| m_z,m_y,0)	(-z,y,0 \| -m_z,m_y,0)	(-y,0,z \| -m_y,0,m_z)
(y,0,z \| m_y,0,m_z)	(0,-y,-z \| 0,-m_y,-m_z)	(0,y,-z \| 0,m_y,-m_z)
(0,-y,z \| 0,-m_y,m_z)	(y,0,-z \| m_y,0,-m_z)	(-y,0,-z \| -m_y,0,-m_z)
(0,z,y \| 0,m_z,m_y)	(0,-z,-y \| 0,-m_z,-m_y)	(z,-y,0 \| m_z,-m_y,0)
(-z,-y,0 \| -m_z,-m_y,0)	(z,0,y \| m_z,0,m_y)	(y,z,0 \| m_y,m_z,0)
(-y,z,0 \| -m_y,m_z,0)	(-z,0,y \| -m_z,0,m_y)	(-y,-z,0 \| -m_y,-m_z,0)
(z,0,-y \| m_z,0,-m_y)	(y,-z,0 \| m_y,-m_z,0)	(-z,0,-y \| -m_z,0,-m_y)

48

i

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

48

h

(0,y,y \| 0,m_y,m_y)	(0,-y,y \| 0,-m_y,m_y)	(0,y,-y \| 0,m_y,-m_y)
(y,y,0 \| m_y,m_y,0)	(-y,y,0 \| -m_y,m_y,0)	(-y,0,y \| -m_y,0,m_y)
(y,0,y \| m_y,0,m_y)	(0,-y,-y \| 0,-m_y,-m_y)	(y,0,-y \| m_y,0,-m_y)
(-y,0,-y \| -m_y,0,-m_y)	(y,-y,0 \| m_y,-m_y,0)	(-y,-y,0 \| -m_y,-m_y,0)

48

g

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

32

f

(x,x,x \| m_x,m_x,m_x)	(x,-x,x \| m_x,-m_x,m_x)	(x,x,-x \| m_x,m_x,-m_x)
(-x,x,x \| -m_x,m_x,m_x)	(x,-x,-x \| m_x,-m_x,-m_x)	(-x,x,-x \| -m_x,m_x,-m_x)
(-x,-x,x \| -m_x,-m_x,m_x)	(-x,-x,-x \| -m_x,-m_x,-m_x)

24

e

(x,0,0 \| m_x,0,0)	(0,0,-x \| 0,0,-m_x)	(0,0,x \| 0,0,m_x)
(0,x,0 \| 0,m_x,0)	(0,-x,0 \| 0,-m_x,0)	(-x,0,0 \| -m_x,0,0)

24

d

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

8

c

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

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

4

b

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

4

a

(0,0,0 | 0,0,0)

Site Symmetries of the Wyckoff Positions

WP	Representative	PG
4a	(0,0,0 \| 0,0,0)	m'-3m'
4b	(1/2,1/2,1/2 \| 0,0,0)	m'-3m'
8c	(1/4,1/4,1/4 \| 0,0,0)	-4'3m'
24d	(0,1/4,1/4 \| 0,0,0)	m'm'm'
24e	(x,0,0 \| m_x,0,0)	4
32f	(x,x,x \| m_x,m_x,m_x)	3
48g	(x,1/4,1/4 \| m_x,0,0)	2
48h	(0,y,y \| 0,m_y,m_y)	2
48i	(1/2,y,y \| 0,m_y,m_y)	2
96j	(0,y,z \| 0,m_y,m_z)	1
96k	(x,x,z \| m_x,m_x,m_z)	1
192l	(x,y,z \| m_x,m_y,m_z)	1

List all the elements of the orbits

Go to the operators of (Fm'-3'm')
Go to the extinction rules of (Fm'-3'm')

Back to the list of magnetic space groups derived from Fm-3m
Back to the list of Magnetic Space Groups

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