Table of Magnetic Space Group Symbols

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Table of Magnetic Space Group Symbols

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P_Cmmn [#59.415] (Type: 4 -- Type IV (klassengleiche))

[OG: C_Pmmm' #65.14.558]

Wyckoff Positions of Group 59.415 (P_Cmmn)

Multiplicity

Wyckoff
letter

Coordinates

16

r

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

8

q

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

8

p

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

8

o

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

8

n

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

8

m

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

4

l

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

4

k

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

4

j

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

4

i

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

4

h

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

4

g

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

4

f

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

4

e

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

2

d

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

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

2

c

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

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

2

b

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

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

2

a

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

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

Site Symmetries of the Wyckoff Positions

WP	Representative	PG
2a	(1/4,1/4,0 \| 0,0,0)	mmm'
2b	(3/4,1/4,0 \| 0,0,0)	mmm'
2c	(3/4,1/4,1/2 \| 0,0,0)	mmm'
2d	(1/4,1/4,1/2 \| 0,0,0)	mmm'
4e	(1/2,1/2,0 \| m_x,m_y,0)	-1
4f	(1/2,1/2,1/2 \| m_x,m_y,0)	-1
4g	(x,1/4,0 \| 0,m_y,0)	m
4h	(x,1/4,1/2 \| 0,m_y,0)	m
4i	(1/4,y,0 \| m_x,0,0)	m
4j	(1/4,y,1/2 \| m_x,0,0)	m
4k	(1/4,1/4,z \| 0,0,0)	mm2
4l	(1/4,3/4,z \| 0,0,0)	mm2
8m	(1/2,1/2,z \| m_x,m_y,0)	1
8n	(1/4,y,z \| m_x,0,0)	m
8o	(x,1/4,z \| 0,m_y,0)	m
8p	(x,y,0 \| m_x,m_y,0)	1
8q	(x,y,1/2 \| m_x,m_y,0)	1
16r	(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 (P_Cmmn)

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