Table of Magnetic Space Group Symbols

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Table of Magnetic Space Group Symbols

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P_I-43n [#218.84] (Type: 4 -- Type IV (klassengleiche))

[OG: I_P-4'3m' #217.5.1584]

Wyckoff Positions of Group 218.84 (P_I-43n)

Multiplicity

Wyckoff
letter

Coordinates

48

h

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

24

g

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

24

f

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

12

e

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

12

d

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

8

c

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

6

b

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

2

a

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

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

Site Symmetries of the Wyckoff Positions

WP	Representative	PG
2a	(0,0,0 \| 0,0,0)	-4'3m'
6b	(0,1/2,1/2 \| 0,0,0)	-4'2m'
8c	(x,x,x \| m_x,m_x,m_x)	3
12d	(1/4,1/2,0 \| m_x,0,0)	-4
12e	(x,0,0 \| m_x,0,0)	2
24f	(x,1/2,0 \| m_x,0,0)	2
24g	(x,x,z \| m_x,m_x,m_z)	1
48h	(x,y,z \| m_x,m_y,m_z)	1

List all the elements of the orbits

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