Chamfered Polyhedron

Author

Eric W. Weisstein
October 5, 2022

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

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

©2022 Wolfram Research, Inc. except for portions noted otherwise

Source

https://resources.wolframcloud.com/FunctionRepository/resources/ChamferedPolyhedron/

Numericizes:

ResourceFunction["ChamferedPolyhedron"][Tetrahedron[],1/2]

PolyhedronCoordinates[%]

Unevaluated for 0 and ≥ 1:

ResourceFunction["ChamferedPolyhedron"][Tetrahedron[],0]

Graphics3D[ResourceFunction["ChamferedPolyhedron"][Tetrahedron[],.999]]

ResourceFunction["ChamferedPolyhedron"][Tetrahedron[],1]

ResourceFunction["ChamferedPolyhedron"][Tetrahedron[],1.1]

Removing the N:

ChamferedPolyhedron[Cube[],1/2]//PolyhedronCoordinates

ChamferedPolyhedron[Cube[],.5`30]//PolyhedronCoordinates

Figure

GraphicsGrid[Graphics3D[{Opacity[.8],#},Boxed->False]&/@Prepend[Table[ResourceFunction["ChamferedPolyhedron"][#,r],{r,.2,.99,.2}],#]&/@{Tetrahedron[],Cube[],Octahedron[],Dodecahedron[],Icosahedron[]},ImageSize->800]

Graphics3D[ResourceFunction["ChamferedPolyhedron"][#,.999]]&/@{Tetrahedron[],Cube[],Octahedron[],Dodecahedron[],Icosahedron[]}

Properties

<<MathWorld`Polyhedra`

A polyhedron with e edges will have a chamfered form containing 2e new vertices, 3e new edges, and e new hexagonal faces.

With[{p=CanonicalizePolyhedron[#]},With[{c=ResourceFunction["ChamferedPolyhedron"][p]},Table[
((PolyhedronCount[c,d]-PolyhedronCount[p,d])/(PolyhedronEdgeCount[p])),
{d,0,2}
]
]]&/@{Tetrahedron[],Cube[],Octahedron[],Dodecahedron[],Icosahedron[]}//Union

Algorithm

Graphics3D[ResourceFunction["ChamferedPolyhedron"][PolyhedronData[{"Pyramid",4},"Polyhedron"],.2]]

For a midscriptable solid

Manipulate[ChamferedPolyhedron[PolyhedronData[p,"Polyhedron"],d]//Graphics3D,{d,.01,10},{p,PolyhedronData["Platonic"]}]