Waterman Polyhedron

Author

Eric W. Weisstein
April 11, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Polyhedra/WatermanPolyhedron.nb.

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

©2006 Wolfram Research, Inc. except for portions noted otherwise

Initialization

Graphics

pts =Drop[Split[Sort[Flatten[Table[{a,b,c},{a,-10,10},{b,-10,10},{c,-10,10}],2],Total[#1^2]<Total[#2^2]&],Total[#1^2]==Total[#2^2]&],1];

Show[GraphicsArray[
Partition[Graphics3D[#,Boxed->False]&/@Table[Map[Polygon[Map[#+8{Mod[s-1,5],Floor[(s-1)/5],0}&,First[#]. RotationMatrix3D[Pi/3,Pi/7,Pi/5] ]] &,ConvexHull3D[Flatten[Take[pts//N,s],1]]],{s,15}],5]],ImageSize->500,GraphicsSpacing->-.1]//Timing