Table of Magnetic Space Group Symbols

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Table of Magnetic Space Group Symbols

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Ia'-3'd' [#230.149] (Type: 3 -- Type III (translationgleiche))

[OG: Ia'-3'd' #230.5.1651]

Wyckoff Positions of Group 230.149 (Ia'-3'd')

Multiplicity

Wyckoff
letter

Coordinates

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

96

h

(x,y,z \| m_x,m_y,m_z)	(x+1/4,-z+1/4,y+3/4 \| m_x,-m_z,m_y)	(x+3/4,z+1/4,-y+1/4 \| m_x,m_z,-m_y)
(z+3/4,y+1/4,-x+1/4 \| m_z,m_y,-m_x)	(-z+1/4,y+3/4,x+1/4 \| -m_z,m_y,m_x)	(-y+1/4,x+3/4,z+1/4 \| -m_y,m_x,m_z)
(y+1/4,-x+1/4,z+3/4 \| m_y,-m_x,m_z)	(x,-y,-z+1/2 \| 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)	(y+3/4,x+1/4,-z+1/4 \| m_y,m_x,-m_z)	(-y+1/4,-x+1/4,-z+1/4 \| -m_y,-m_x,-m_z)
(-x+1/4,z+3/4,y+1/4 \| -m_x,m_z,m_y)	(-x+1/4,-z+1/4,-y+1/4 \| -m_x,-m_z,-m_y)	(z+1/4,-y+1/4,x+3/4 \| m_z,-m_y,m_x)
(-z+1/4,-y+1/4,-x+1/4 \| -m_z,-m_y,-m_x)	(z,x,y \| m_z,m_x,m_y)	(y,z,x \| m_y,m_z,m_x)
(-y+1/2,z,-x \| -m_y,m_z,-m_x)	(-z,-x+1/2,y \| -m_z,-m_x,m_y)	(-y,-z+1/2,x \| -m_y,-m_z,m_x)
(z,-x,-y+1/2 \| m_z,-m_x,-m_y)	(y,-z,-x+1/2 \| m_y,-m_z,-m_x)	(-z+1/2,x,-y \| -m_z,m_x,-m_y)
(-x,-y,-z \| -m_x,-m_y,-m_z)	(-x+1/4,z+1/4,-y+3/4 \| -m_x,m_z,-m_y)	(-x+3/4,-z+1/4,y+1/4 \| -m_x,-m_z,m_y)
(-z+3/4,-y+1/4,x+1/4 \| -m_z,-m_y,m_x)	(z+1/4,-y+3/4,-x+1/4 \| m_z,-m_y,-m_x)	(y+1/4,-x+3/4,-z+1/4 \| m_y,-m_x,-m_z)
(-y+1/4,x+1/4,-z+3/4 \| -m_y,m_x,-m_z)	(-x,y,z+1/2 \| -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)	(-y+3/4,-x+1/4,z+1/4 \| -m_y,-m_x,m_z)	(y+1/4,x+1/4,z+1/4 \| m_y,m_x,m_z)
(x+1/4,-z+3/4,-y+1/4 \| m_x,-m_z,-m_y)	(x+1/4,z+1/4,y+1/4 \| m_x,m_z,m_y)	(-z+1/4,y+1/4,-x+3/4 \| -m_z,m_y,-m_x)
(z+1/4,y+1/4,x+1/4 \| m_z,m_y,m_x)	(-z,-x,-y \| -m_z,-m_x,-m_y)	(-y,-z,-x \| -m_y,-m_z,-m_x)
(y+1/2,-z,x \| m_y,-m_z,m_x)	(z,x+1/2,-y \| m_z,m_x,-m_y)	(y,z+1/2,-x \| m_y,m_z,-m_x)
(-z,x,y+1/2 \| -m_z,m_x,m_y)	(-y,z,x+1/2 \| -m_y,m_z,m_x)	(z+1/2,-x,y \| m_z,-m_x,m_y)

48

g

(1/8,y,-y+1/4 \| 0,m_y,-m_y)	(3/8,y,y+3/4 \| 0,m_y,m_y)	(7/8,-y+1/2,-y+1/4 \| 0,-m_y,-m_y)
(-y,y+1/4,1/8 \| -m_y,m_y,0)	(y,y+3/4,3/8 \| m_y,m_y,0)	(-y+1/4,7/8,-y+1/2 \| -m_y,0,-m_y)
(y+1/4,1/8,-y \| m_y,0,-m_y)	(1/8,-y,y+1/4 \| 0,-m_y,m_y)	(y+3/4,3/8,y \| m_y,0,m_y)
(-y+1/4,1/8,y \| -m_y,0,m_y)	(-y+1/2,-y+1/4,7/8 \| -m_y,-m_y,0)	(y,-y+1/4,1/8 \| m_y,-m_y,0)
(7/8,-y,y+3/4 \| 0,-m_y,m_y)	(5/8,-y,-y+1/4 \| 0,-m_y,-m_y)	(1/8,y+1/2,y+3/4 \| 0,m_y,m_y)
(y,-y+3/4,7/8 \| m_y,-m_y,0)	(-y,-y+1/4,5/8 \| -m_y,-m_y,0)	(y+3/4,1/8,y+1/2 \| m_y,0,m_y)
(-y+3/4,7/8,y \| -m_y,0,m_y)	(7/8,y,-y+3/4 \| 0,m_y,-m_y)	(-y+1/4,5/8,-y \| -m_y,0,-m_y)
(y+3/4,7/8,-y \| m_y,0,-m_y)	(y+1/2,y+3/4,1/8 \| m_y,m_y,0)	(-y,y+3/4,7/8 \| -m_y,m_y,0)

48

f

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

32

e

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

24

d

(3/8,0,1/4 \| 0,0,0)	(5/8,0,3/4 \| 0,0,0)	(0,1/4,7/8 \| 0,0,0)
(0,3/4,5/8 \| 0,0,0)	(1/4,1/8,1/2 \| 0,0,0)	(1/4,7/8,0 \| 0,0,0)
(1/8,0,3/4 \| 0,0,0)	(7/8,0,1/4 \| 0,0,0)	(1/4,3/8,0 \| 0,0,0)
(0,1/4,3/8 \| 0,0,0)	(0,3/4,1/8 \| 0,0,0)	(1/4,5/8,1/2 \| 0,0,0)

24

c

(1/8,0,1/4 \| 0,0,0)	(3/8,0,3/4 \| 0,0,0)	(0,1/4,1/8 \| 0,0,0)
(0,3/4,3/8 \| 0,0,0)	(1/4,7/8,1/2 \| 0,0,0)	(1/4,1/8,0 \| 0,0,0)
(7/8,0,3/4 \| 0,0,0)	(5/8,0,1/4 \| 0,0,0)	(0,3/4,7/8 \| 0,0,0)
(0,1/4,5/8 \| 0,0,0)	(3/4,1/8,1/2 \| 0,0,0)	(3/4,7/8,0 \| 0,0,0)

16

b

(1/8,1/8,1/8 \| 0,0,0)	(3/8,1/8,7/8 \| 0,0,0)	(7/8,3/8,1/8 \| 0,0,0)
(1/8,7/8,3/8 \| 0,0,0)	(7/8,7/8,7/8 \| 0,0,0)	(5/8,7/8,1/8 \| 0,0,0)
(1/8,5/8,7/8 \| 0,0,0)	(7/8,1/8,5/8 \| 0,0,0)

16

a

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

Site Symmetries of the Wyckoff Positions

WP	Representative	PG
16a	(0,0,0 \| 0,0,0)	-3'
16b	(1/8,1/8,1/8 \| 0,0,0)	32
24c	(1/8,0,1/4 \| 0,0,0)	222
24d	(3/8,0,1/4 \| 0,0,0)	-4'
32e	(x,x,x \| m_x,m_x,m_x)	3
48f	(x,0,1/4 \| m_x,0,0)	2
48g	(1/8,y,-y+1/4 \| 0,m_y,-m_y)	2
96h	(x,y,z \| m_x,m_y,m_z)	1

List all the elements of the orbits

Go to the operators of (Ia'-3'd')
Go to the extinction rules of (Ia'-3'd')

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