Table of Magnetic Space Group Symbols

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Table of Magnetic Space Group Symbols

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R-3'm' [#166.100] (Type: 3 -- Type III (translationgleiche))

[OG: R-3'm' #166.4.1330]

Wyckoff Positions of Group 166.100 (R-3'm')

Multiplicity

Wyckoff
letter

Coordinates

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

36

i

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

18

h

(x,-x,z \| m_x,-m_x,m_z)	(x,2x,z \| m_x,2m_x,m_z)	(-2x,-x,z \| -2m_x,-m_x,m_z)
(2x,x,-z \| 2m_x,m_x,-m_z)	(-x,x,-z \| -m_x,m_x,-m_z)	(-x,-2x,-z \| -m_x,-2m_x,-m_z)

18

g

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

18

f

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

9

e

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

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

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

9

d

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

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

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

6

c

(0,0,z | 0,0,m_z)

(0,0,-z | 0,0,-m_z)

3

b

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

3

a

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

Site Symmetries of the Wyckoff Positions

WP	Representative	PG
3a	(0,0,0 \| 0,0,0)	-3'm'
3b	(0,0,1/2 \| 0,0,0)	-3'm'
6c	(0,0,z \| 0,0,m_z)	3
9d	(1/2,0,1/2 \| 0,0,0)	2/m'
9e	(1/2,0,0 \| 0,0,0)	2/m'
18f	(x,0,0 \| m_x,0,0)	2
18g	(x,0,1/2 \| m_x,0,0)	2
18h	(x,-x,z \| m_x,-m_x,m_z)	1
36i	(x,y,z \| m_x,m_y,m_z)	1

List all the elements of the orbits

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

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