Plane of Symmetry

Author

Eric W. Weisstein
August 14, 2026

This notebook downloaded from https://mathworld.wolfram.com/notebooks/SolidGeometry/PlaneofSymmetry.nb.

For more information, see Eric's MathWorld entry https://mathworld.wolfram.com/PlaneofSymmetry.html.

©2026 Wolfram Research, Inc. except for portions noted otherwise

Illustration

Reflection in the blue plane W maps the cube onto itself.

Module[{labelBackground,neutral,planeColor,symmetryPlane},neutral=LightDarkSwitched[Black,White];labelBackground=LightDarkSwitched[White,Black];planeColor=Blue;symmetryPlane={{0,-(13/10),-(13/10)},{0,(13/10),-(13/10)},{0,(13/10),(13/10)},{0,-(13/10),(13/10)}};Graphics3D[{Directive[StandardGray,Opacity[0.18]],Cuboid[{-1,-1,-1},{1,1,1}],Directive[neutral,Opacity[1],AbsoluteThickness[1.5]],Line[{{-1,-1,-1},{1,-1,-1},{1,1,-1},{-1,1,-1},{-1,-1,-1}}],Line[{{-1,-1,1},{1,-1,1},{1,1,1},{-1,1,1},{-1,-1,1}}],Line[{{-1,-1,-1},{-1,-1,1}}],Line[{{1,-1,-1},{1,-1,1}}],Line[{{1,1,-1},{1,1,1}}],Line[{{-1,1,-1},{-1,1,1}}],Directive[planeColor,Opacity[0.28]],Polygon[symmetryPlane],Directive[planeColor,Opacity[1],AbsoluteThickness[2]],Line[Append[symmetryPlane,First[symmetryPlane]]],Text[Style[W,18,planeColor,FontFamily->"Times",Background->labelBackground],{0,(7/5),(7/5)}]},Boxed->False]]