TOPICS

# Chamfered Polyhedron

A chamfered polyhedron, also known as an egde-truncated polyhedron, is a polyhedron constructed from an original polyhedron by moving faces outward while retaining the original vertices, thus creating a new (in general not regular) hexagon in place of each original edge. More specifically, chamfering is the truncation of each edge of a polyhedron with the plane perpendicular to the plane bisecting the dihedral angle between two faces, effectively replacing each original edge with a hexagonal face (Mangaldan 2021). The illustration above shows increasing amounts of chamfering applied to the Platonic solids.

It is possible to create equilateral chamfered versions of the Platonic solids by appropriate choice of the edge length ratio for chamfering.

For an original polyhedron with edges, its chamfered version contains additional vertices, additional edges, and additional (in general not regular) hexagonal faces.

Chamfered Cube, Chamfered Dodecahedron, Chamfered Icosahedron, Chamfered Octahedron, Chamfered Tetrahedron

## References

Mangaldan, J. "ChamferedPolyhedron." Sep. 21, 2021. https://resources.wolframcloud.com/FunctionRepository/resources/ChamferedPolyhedron/.McCooey, D. I. "Chamfered Solids." http://dmccooey.com/polyhedra/Chamfer.html.

## Cite this as:

Weisstein, Eric W. "Chamfered Polyhedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ChamferedPolyhedron.html