Table of Magnetic Space Group Symbols

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Table of Magnetic Space Group Symbols

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P4/mm'm' [#123.345] (Type: 3 -- Type III (translationgleiche))

[OG: P4/mm'm' #123.7.1005]

Wyckoff Positions of Group 123.345 (P4/mm'm')

Multiplicity

Wyckoff
letter

Coordinates

16

u

(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,-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,-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,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)

8

t

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

8

s

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

8

r

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

8

q

(x,y,1/2 \| 0,0,m_z)	(-y,x,1/2 \| 0,0,m_z)	(y,-x,1/2 \| 0,0,m_z)
(x,-y,1/2 \| 0,0,m_z)	(-x,y,1/2 \| 0,0,m_z)	(-x,-y,1/2 \| 0,0,m_z)
(y,x,1/2 \| 0,0,m_z)	(-y,-x,1/2 \| 0,0,m_z)

8

p

(x,y,0 \| 0,0,m_z)	(-y,x,0 \| 0,0,m_z)	(y,-x,0 \| 0,0,m_z)
(x,-y,0 \| 0,0,m_z)	(-x,y,0 \| 0,0,m_z)	(-x,-y,0 \| 0,0,m_z)
(y,x,0 \| 0,0,m_z)	(-y,-x,0 \| 0,0,m_z)

4

o

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

4

n

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

4

m

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

4

l

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

4

k

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

4

j

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

4

i

(0,1/2,z \| 0,0,m_z)	(1/2,0,z \| 0,0,m_z)	(0,1/2,-z \| 0,0,m_z)
(1/2,0,-z \| 0,0,m_z)

2

h

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

(1/2,1/2,-z | 0,0,m_z)

2

g

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

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

2

f

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

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

2

e

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

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

1

d

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

1

c

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

1

b

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

1

a

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

Site Symmetries of the Wyckoff Positions

WP	Representative	PG
1a	(0,0,0 \| 0,0,m_z)	4/m
1b	(0,0,1/2 \| 0,0,m_z)	4/m
1c	(1/2,1/2,0 \| 0,0,m_z)	4/m
1d	(1/2,1/2,1/2 \| 0,0,m_z)	4/m
2e	(0,1/2,1/2 \| 0,0,m_z)	2/m
2f	(0,1/2,0 \| 0,0,m_z)	2/m
2g	(0,0,z \| 0,0,m_z)	4
2h	(1/2,1/2,z \| 0,0,m_z)	4
4i	(0,1/2,z \| 0,0,m_z)	2
4j	(x,x,0 \| 0,0,m_z)	m
4k	(x,x,1/2 \| 0,0,m_z)	m
4l	(x,0,0 \| 0,0,m_z)	m
4m	(x,0,1/2 \| 0,0,m_z)	m
4n	(x,1/2,0 \| 0,0,m_z)	m
4o	(x,1/2,1/2 \| 0,0,m_z)	m
8p	(x,y,0 \| 0,0,m_z)	m
8q	(x,y,1/2 \| 0,0,m_z)	m
8r	(x,x,z \| m_x,m_x,m_z)	1
8s	(x,0,z \| m_x,0,m_z)	1
8t	(x,1/2,z \| m_x,0,m_z)	1
16u	(x,y,z \| m_x,m_y,m_z)	1

List all the elements of the orbits

Go to the operators of (P4/mm'm')
Go to the extinction rules of (P4/mm'm')

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