Wyckoff Positions of Magnetic Space Groups

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Wyckoff Positions of the Group F_Sd-3c (#228.139) [BNS setting]

228.139 Fd-3c.1'_I[Pn-3m] (UNI symbol)

To display the Wyckoff positions in the OG setting, please follow this link: P_Fn-3m' ( #224.7.1617)

Multiplicity

Wyckoff
letter

Coordinates

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

384

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

192

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

192

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

192

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

192

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

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

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

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

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

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

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

(3/8,3/8,7/8 | 0,0,0)

(1/8,1/8,5/8 | 0,0,0)

Site Symmetries of the Wyckoff Positions

WP	Representative	Site symmetry
16a	(3/8,3/8,7/8 \| 0,0,0)	-4'3m'
32b	(1/4,1/4,0 \| m_x,m_x,-m_x)	.-3m'
32c	(1/2,1/2,3/4 \| 0,0,0)	.-3'm'
48d	(5/8,3/8,5/8 \| 0,m_y,0)	-42'.m'
64e	(x,x,-x+1/4 \| m_x,m_x,-m_x)	.3m'
96f	(3/8,1/2,5/8 \| m_x,0,m_x)	2'.22'
96g	(3/8,y,7/8 \| 0,m_y,0)	2.m'm'
192h	(3/8,y,5/8 \| m_x,0,m_z)	2'..
192i	(x,1/2,-x \| m_x,m_y,m_x)	..2'
192j	(x,1/2,x+3/4 \| m_x,0,m_x)	..2
192k	(x,x,z \| m_x,m_x,m_z)	..m'
384l	(x,y,z \| m_x,m_y,m_z)	1

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List all the elements of the orbits

Go to the list of the Symmetry Operators of the Group F_Sd-3c (#228.139)
Go to the Systematic absences for the Group F_Sd-3c (#228.139)

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Wyckoff Positions of the Group FSd-3c (#228.139) [BNS setting]

Site Symmetries of the Wyckoff Positions

Wyckoff Positions of the Group F_Sd-3c (#228.139) [BNS setting]