Wyckoff Positions of Magnetic Space Groups

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Wyckoff Positions of Magnetic Space Groups

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Wyckoff Positions of the Group P6₃'/m'cm' (#193.259)
**193.259 P6₃'/m'cm' (UNI symbol)**

For this space group, BNS and OG settings coincide.
Its label in the OG setting is given as: P6₃'/m'cm' (#193.7.1491)

Multiplicity

Wyckoff
letter

Coordinates

24

l

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

12

k

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

12

j

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

12

i

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

8

h

(1/3,2/3,z \| 0,0,m_z)	(2/3,1/3,z+1/2 \| 0,0,-m_z)
(2/3,1/3,-z+1/2 \| 0,0,-m_z)	(1/3,2/3,-z \| 0,0,m_z)
(2/3,1/3,-z \| 0,0,m_z)	(1/3,2/3,-z+1/2 \| 0,0,-m_z)
(1/3,2/3,z+1/2 \| 0,0,-m_z)	(2/3,1/3,z \| 0,0,m_z)

6

g

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

6

f

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

4

e

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

4

d

(1/3,2/3,0 \| 0,0,m_z)	(2/3,1/3,1/2 \| 0,0,-m_z)
(2/3,1/3,0 \| 0,0,m_z)	(1/3,2/3,1/2 \| 0,0,-m_z)

4

c

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

2

b

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

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

2

a

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

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

Site Symmetries of the Wyckoff Positions

WP	Representative	Site symmetry
2a	(0,0,1/4 \| 0,0,0)	-6'2m'
2b	(0,0,0 \| 0,0,m_z)	-3.m'
4c	(1/3,2/3,1/4 \| 0,0,0)	-6'..
4d	(1/3,2/3,0 \| 0,0,m_z)	3.2'
4e	(0,0,z \| 0,0,m_z)	3.m'
6f	(1/2,0,0 \| m_x,0,m_z)	..2'/m'
6g	(x,0,1/4 \| m_x,0,0)	m'2m'
8h	(1/3,2/3,z \| 0,0,m_z)	3..
12i	(x,2x,0 \| m_x,0,m_z)	..2'
12j	(x,y,1/4 \| m_x,m_y,0)	m'..
12k	(x,0,z \| m_x,0,m_z)	..m'
24l	(x,y,z \| m_x,m_y,m_z)	1

List the original elements of the orbits
List all the elements of the orbits

Go to the list of the Symmetry Operators of the Group P6₃'/m'cm' (#193.259)
Go to the Systematic absences for the Group P6₃'/m'cm' (#193.259)

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