Rectification

Author

Eric W. Weisstein
February 1, 2011

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

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

©2010 Wolfram Research, Inc. except for portions noted otherwise

Graphic

g1={
Show[Graphics3D[{
v=PolyhedronData[#,"Faces"],
vf=VertexFigures[Normal[PolyhedronData[#,"Faces"]]]}],
Boxed->False
],
Graphics3D[
ConvexHull3D[Flatten[vf[[All,1]],1]],
Boxed->False,
PlotRange->Function[mm,Through[{Min,Max}[mm]]]/@Transpose[Flatten[Normal[PolyhedronData[#,"Faces"]][[1,All,1]],1]]
]}&/@{"Tetrahedron","Cube","Octahedron"}

g2={
Show[Graphics3D[{
v=PolyhedronData[#,"Faces"],
vf=VertexFigures[Normal[PolyhedronData[#,"Faces"]]]}],
Boxed->False
],
Graphics3D[
ConvexHull3D[Flatten[vf[[All,1]],1]],
Boxed->False,
PlotRange->Function[mm,Through[{Min,Max}[mm]]]/@Transpose[Flatten[Normal[PolyhedronData[#,"Faces"]][[1,All,1]],1]]
]}&/@{"Dodecahedron","Icosahedron"}//Quiet

GraphicsGrid[{
Join[g1[[1]],{""},g2[[1]]],
Join[g1[[2]],{""},g2[[2]]],
Join[g1[[3]]]
}]

"Rectification"->,

Graphics3D[VertexFigures[Normal[PolyhedronData["Cube","Faces"]]]]