Pensieve header: Drawing a permutohedron. Continues pensieve://2009-10/.

SetDirectory["C:\\drorbn\\AcademicPensieve\\Classes\\23-FastComputations\\KH4Knots"]

pts4= Point @@@ Permutations[Range[4]]

mat={{1,-1,0,0}, {0,1,-1,0}, {0,0,1,-1}};mat=Drop[Orthogonalize[{{1,1,1,1},{1,-1,0,0}, {0,1,-1,0}, {0,0,1,-1}}], 1]

pts3=pts4 /. Point[xs__] :> Point @@ (
mat.{xs}
)

Permutohedron=Rasterize@Graphics3D[ConvexHullMesh[pts3/.Point->List],{Boxed->False,ImageSize->{359.635,357.951},ImageSizeRaw->Automatic,ViewPoint->{2.76216,1.27727,1.47954},ViewVertical->{0.0144266,0.597172,0.801984}}]

Export["Permutohedron.png",ImageCrop@Permutahedron]