Polyhedra

Math 282 Computational Geometry

Truncated Cube

Graphics3D[{Opacity[0.9],EdgeForm[Thick],PolyhedronData["TruncatedCube","Polygons"]},Boxed->False]

Small Rhombicuboctahedron

Graphics3D[{Opacity[0.9],EdgeForm[Thick],PolyhedronData["SmallRhombicuboctahedron","Polygons"]},Boxed->False]

A Polyhedron with a Hole

𝒫1=Polyhedron[{{0,0,0},{3,0,0},{3,0,1},{0,0,1},{0,3,0},{3,3,0},{3,3,1},{0,3,1},{1,1,1/2},{2,1,1/2},{2,2,1/2},{1,2,1/2}},{{1,2,3,4},{2,3,7,6},{5,6,7,8},{1,4,8,5},{1,2,10,9},{4,3,10,9},{2,6,11,10},{3,7,11,10},{5,6,11,12},{8,7,11,12},{1,5,12,9},{4,8,12,9}}];
Graphics3D[{Opacity[0.9],EdgeForm[Thick],𝒫1},Boxed->False]

A Polyhedron with Two Holes

𝒫2=Polygon[{{0,0,0},{2√3,2,0},{0,4,0},{-2√3,2,0},{0,0,1},{2√3,2,1},{0,4,1},{-2√3,2,1},{3/4,3√3/4,1/2},{2√3-3/2,2,1/2},{3/4,4-3√3/4,1/2},{-3/4,3√3/4,1/2},{-2√3+3/2,2,1/2},{-3/4,4-3√3/4,1/2}},{{1,2,6,5},{2,3,7,6},{3,4,8,7},{1,4,8,5},{1,2,10,9},{5,6,10,9},{2,3,11,10},{6,7,11,10},{1,3,11,9},{5,7,11,9},{1,4,13,12},{5,8,13,12},{1,3,14,12},{5,7,14,12},{3,4,13,14},{7,8,13,14}}];
Graphics3D[{Opacity[0.9],EdgeForm[Thick],𝒫2},Boxed->False]

Great Rhombicuboctahedron

Graphics3D[{Opacity[0.9],EdgeForm[Thick],PolyhedronData["GreatRhombicuboctahedron","Polygons"]},Boxed->False]