Table of Magnetic Space Group Symbols

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Table of Magnetic Space Group Symbols

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Fd'-3'm' [#227.132] (Type: 3 -- Type III (translationgleiche))

[OG: Fd'-3'm' #227.5.1632]

Wyckoff Positions of Group 227.132 (Fd'-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

i

(x,y,z \| m_x,m_y,m_z)	(x+1/4,-z,y+1/4 \| m_x,-m_z,m_y)	(x+1/4,z+1/4,-y \| m_x,m_z,-m_y)
(z+1/4,y+1/4,-x \| m_z,m_y,-m_x)	(-z,y+1/4,x+1/4 \| -m_z,m_y,m_x)	(-y,x+1/4,z+1/4 \| -m_y,m_x,m_z)
(y+1/4,-x,z+1/4 \| m_y,-m_x,m_z)	(x,-y+1/4,-z+1/4 \| m_x,-m_y,-m_z)	(-x+1/4,y,-z+1/4 \| -m_x,m_y,-m_z)
(-x+1/4,-y+1/4,z \| -m_x,-m_y,m_z)	(y+1/4,x+1/4,-z \| m_y,m_x,-m_z)	(-y,-x,-z \| -m_y,-m_x,-m_z)
(-x,z+1/4,y+1/4 \| -m_x,m_z,m_y)	(-x,-z,-y \| -m_x,-m_z,-m_y)	(z+1/4,-y,x+1/4 \| 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+1/4,z,-x+1/4 \| -m_y,m_z,-m_x)	(-z+1/4,-x+1/4,y \| -m_z,-m_x,m_y)	(-y+1/4,-z+1/4,x \| -m_y,-m_z,m_x)
(z,-x+1/4,-y+1/4 \| m_z,-m_x,-m_y)	(y,-z+1/4,-x+1/4 \| m_y,-m_z,-m_x)	(-z+1/4,x,-y+1/4 \| -m_z,m_x,-m_y)
(-x,-y,-z \| -m_x,-m_y,-m_z)	(-x+1/4,z,-y+1/4 \| -m_x,m_z,-m_y)	(-x+1/4,-z+1/4,y \| -m_x,-m_z,m_y)
(-z+1/4,-y+1/4,x \| -m_z,-m_y,m_x)	(z,-y+1/4,-x+1/4 \| m_z,-m_y,-m_x)	(y,-x+1/4,-z+1/4 \| m_y,-m_x,-m_z)
(-y+1/4,x,-z+1/4 \| -m_y,m_x,-m_z)	(-x,y+1/4,z+1/4 \| -m_x,m_y,m_z)	(x+1/4,-y,z+1/4 \| m_x,-m_y,m_z)
(x+1/4,y+1/4,-z \| m_x,m_y,-m_z)	(-y+1/4,-x+1/4,z \| -m_y,-m_x,m_z)	(y,x,z \| m_y,m_x,m_z)
(x,-z+1/4,-y+1/4 \| m_x,-m_z,-m_y)	(x,z,y \| m_x,m_z,m_y)	(-z+1/4,y,-x+1/4 \| -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+1/4,-z,x+1/4 \| m_y,-m_z,m_x)	(z+1/4,x+1/4,-y \| m_z,m_x,-m_y)	(y+1/4,z+1/4,-x \| m_y,m_z,-m_x)
(-z,x+1/4,y+1/4 \| -m_z,m_x,m_y)	(-y,z+1/4,x+1/4 \| -m_y,m_z,m_x)	(z+1/4,-x,y+1/4 \| m_z,-m_x,m_y)

96

h

(0,y,-y \| 0,m_y,-m_y)	(1/4,y,y+1/4 \| 0,m_y,m_y)	(1/4,-y+1/4,-y \| 0,-m_y,-m_y)
(-y+1/4,y+1/4,0 \| -m_y,m_y,0)	(y,y+1/4,1/4 \| m_y,m_y,0)	(-y,1/4,-y+1/4 \| -m_y,0,-m_y)
(y+1/4,0,-y+1/4 \| m_y,0,-m_y)	(0,-y+1/4,y+1/4 \| 0,-m_y,m_y)	(y+1/4,1/4,y \| m_y,0,m_y)
(-y,0,y \| -m_y,0,m_y)	(-y+1/4,-y,1/4 \| -m_y,-m_y,0)	(y,-y,0 \| m_y,-m_y,0)
(0,-y,y \| 0,-m_y,m_y)	(1/4,-y,-y+1/4 \| 0,-m_y,-m_y)	(1/4,y+1/4,y \| 0,m_y,m_y)
(y+1/4,-y+1/4,0 \| m_y,-m_y,0)	(-y,-y+1/4,1/4 \| -m_y,-m_y,0)	(y,1/4,y+1/4 \| m_y,0,m_y)
(-y+1/4,0,y+1/4 \| -m_y,0,m_y)	(0,y+1/4,-y+1/4 \| 0,m_y,-m_y)	(-y+1/4,1/4,-y \| -m_y,0,-m_y)
(y,0,-y \| m_y,0,-m_y)	(y+1/4,y,1/4 \| m_y,m_y,0)	(-y,y,0 \| -m_y,m_y,0)

96

g

(x,x,z \| m_x,m_x,m_z)	(x+1/4,-z,x+1/4 \| m_x,-m_z,m_x)	(x+1/4,z+1/4,-x \| m_x,m_z,-m_x)
(z+1/4,x+1/4,-x \| m_z,m_x,-m_x)	(-z,x+1/4,x+1/4 \| -m_z,m_x,m_x)	(-x,x+1/4,z+1/4 \| -m_x,m_x,m_z)
(x+1/4,-x,z+1/4 \| m_x,-m_x,m_z)	(x,-x+1/4,-z+1/4 \| m_x,-m_x,-m_z)	(-x+1/4,x,-z+1/4 \| -m_x,m_x,-m_z)
(-x+1/4,-x+1/4,z \| -m_x,-m_x,m_z)	(x+1/4,x+1/4,-z \| m_x,m_x,-m_z)	(-x,-x,-z \| -m_x,-m_x,-m_z)
(-x,z+1/4,x+1/4 \| -m_x,m_z,m_x)	(-x,-z,-x \| -m_x,-m_z,-m_x)	(z+1/4,-x,x+1/4 \| 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+1/4,z,-x+1/4 \| -m_x,m_z,-m_x)	(-z+1/4,-x+1/4,x \| -m_z,-m_x,m_x)	(-x+1/4,-z+1/4,x \| -m_x,-m_z,m_x)
(z,-x+1/4,-x+1/4 \| m_z,-m_x,-m_x)	(x,-z+1/4,-x+1/4 \| m_x,-m_z,-m_x)	(-z+1/4,x,-x+1/4 \| -m_z,m_x,-m_x)

48

f

(x,1/8,1/8 \| m_x,0,0)	(x+1/4,7/8,3/8 \| m_x,0,0)	(7/8,7/8,-x \| 0,0,-m_x)
(7/8,3/8,x+1/4 \| 0,0,m_x)	(7/8,x+1/4,3/8 \| 0,m_x,0)	(7/8,-x,7/8 \| 0,-m_x,0)
(-x+1/4,1/8,1/8 \| -m_x,0,0)	(-x,7/8,7/8 \| -m_x,0,0)	(1/8,x,1/8 \| 0,m_x,0)
(1/8,1/8,x \| 0,0,m_x)	(1/8,1/8,-x+1/4 \| 0,0,-m_x)	(1/8,-x+1/4,1/8 \| 0,-m_x,0)

32

e

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

16

d

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

16

c

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

8

b

(3/8,3/8,3/8 | 0,0,0)

(5/8,5/8,5/8 | 0,0,0)

8

a

(1/8,1/8,1/8 | 0,0,0)

(7/8,7/8,7/8 | 0,0,0)

Site Symmetries of the Wyckoff Positions

WP	Representative	PG
8a	(1/8,1/8,1/8 \| 0,0,0)	-4'3m'
8b	(3/8,3/8,3/8 \| 0,0,0)	-4'3m'
16c	(0,0,0 \| 0,0,0)	-3'm'
16d	(1/2,1/2,1/2 \| 0,0,0)	-3'm'
32e	(x,x,x \| m_x,m_x,m_x)	3
48f	(x,1/8,1/8 \| m_x,0,0)	2
96g	(x,x,z \| m_x,m_x,m_z)	1
96h	(0,y,-y \| 0,m_y,-m_y)	2
192i	(x,y,z \| m_x,m_y,m_z)	1

List all the elements of the orbits

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

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

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