Cantellation (geometry)

A cantellated cube - Red faces are reduced. Edges are bevelled, forming new yellow square faces. Vertices are truncated, forming new blue triangle faces.

In geometry, a cantellation is a 2nd order truncation in any dimension that bevels a regular polytope at its edges and at its vertices, creating a new facet in place of each edge and of each vertex. Cantellation also applies to regular tilings and honeycombs. Cantellating is also rectifying its rectification.

Cantellation (for polyhedra and tilings) is also called expansion by Alicia Boole Stott: it corresponds to moving the faces of the regular form away from the center, and filling in a new face in the gap for each opened edge and for each opened vertex.

For polyhedra, a cantellation offers a direct sequence from a regular polyhedron to its dual.

For higher-dimensional polytopes, a cantellation offers a direct sequence from a regular polytope to its birectified form.