Coplanar

Author

Eric W. Weisstein
April 8, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SolidGeometry/Coplanar.nb.

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

©2005 Wolfram Research, Inc. except for portions noted otherwise

Examples

CoplanarQ[v_List?MatrixQ,eps_:10^-6]:=True /;Length[v]==3

CoplanarQ[v_List?MatrixQ,eps_:10^-6]:=Module[{n=Cross[v[[2]]-v[[1]],v[[3]]-v[[1]]]},
And@@(Abs[n.(v[[1]]-#)]<eps&/@Drop[v,3])
] /;Length[v]>3

<<Platonic`;
<<Archimedean`;

And@@@Table[CoplanarQ/@First/@Platonic[n],{n,5}]//Timing

And@@@Table[CoplanarQ/@First/@Archimedean[n],{n,13}]//Timing