Table of Magnetic Space Group Symbols

Bilbao Crystallographic Server

MGENPOS

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P_In-3m [#224.115] (Type: 4 -- Type IV (klassengleiche))

[OG: I_Pm'-3'm #229.7.1644]

Wyckoff Positions of Group 224.115 (P_In-3m)

Multiplicity

Wyckoff
letter

Coordinates

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

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

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

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

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

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

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

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

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

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

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

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

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

Site Symmetries of the Wyckoff Positions

WP	Representative	PG
2a	(3/4,3/4,3/4 \| 0,0,0)	m'-3m
6b	(3/4,1/4,1/4 \| 0,0,0)	4'/m'm'm
8c	(0,0,0 \| 0,0,0)	-3m
12d	(0,3/4,1/4 \| 0,0,0)	-4'2m'
12e	(x,3/4,3/4 \| 0,0,0)	4'mm'
16f	(x,x,x \| 0,0,0)	3m
24g	(x,3/4,1/4 \| m_x,0,0)	2
24h	(3/4,y,y \| 0,m_y,-m_y)	m
48i	(0,y,-y \| 0,m_y,-m_y)	2
48j	(3/4,y,z \| 0,m_y,m_z)	1
48k	(x,x,z \| m_x,-m_x,0)	m
96l	(x,y,z \| m_x,m_y,m_z)	1

List all the elements of the orbits

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PIn-3m [#224.115] (Type: 4 -- Type IV (klassengleiche))

[OG: IPm'-3'm #229.7.1644]

Wyckoff Positions of Group 224.115 (PIn-3m)

Site Symmetries of the Wyckoff Positions

P_In-3m [#224.115] (Type: 4 -- Type IV (klassengleiche))

[OG: I_Pm'-3'm #229.7.1644]

Wyckoff Positions of Group 224.115 (P_In-3m)