Mirror Symmetry

Author

Eric W. Weisstein
August 14, 2026

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

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

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

Illustration

Reflection in the plane W maps s to its mirror image s'; the vector n is normal to W.

Module[{axisColor,labelBackground,mirrorPoint,neutral,plane,point,pointColor},neutral=LightDarkSwitched[Black,White];labelBackground=None;axisColor=Blue;pointColor=Red;point={1,(1/2),(1/5)};mirrorPoint={-1,(1/2),(1/5)};plane={{0,-(6/5),-1},{0,(6/5),-1},{0,(6/5),1},{0,-(6/5),1}};
Graphics3D[
{
Directive[StandardGray,Opacity[0.8]],Polygon[plane],
Directive[neutral,Opacity[1],AbsoluteThickness[1.5]],Line[Append[plane,First[plane]]],
{Directive[pointColor,AbsoluteThickness[2],Dashing[{0.025,0.018}]],Line[{point,mirrorPoint}]},
Directive[pointColor,PointSize[0.022]],Point[{point,mirrorPoint}],Directive[axisColor,AbsoluteThickness[2]],
Arrow[{{0,0,0},{(4/5),0,0}}],
Text[Style["W",Italic,18,neutral,FontFamily->"Times",Background->labelBackground],{0,-(4/5),-(3/5)}],Text[Style["n",Bold,18,axisColor,FontFamily->"Times",Background->labelBackground],{.9,0,0}],Text[Style["s",18,Italic,pointColor,FontFamily->"Times",Background->labelBackground],point+{(1/10),0,(1/5)}],Text[Style[Superscript["s","′"],Italic,18,pointColor,FontFamily->"Times",Background->labelBackground],mirrorPoint+{-(1/10),0,(1/5)}]},Boxed->False]]