Truncation (geometry)

In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex.

The term originates from Kepler's names for the Archimedean solids.

A special kind of truncation, usually implied, is a uniform truncation, a truncation operator applied to a regular polyhedron (or regular polytope) which creates a resulting uniform polyhedron (uniform polytope) with equal edge lengths.

There are no degrees of freedom, and it represents a fixed geometric, just like the regular polyhedra.

A complete truncation (or rectification), r{3}, is another regular polygon in its dual position.

A truncated pentagram {5/2} will look like a pentagon, but is actually a double-covered (degenerate) decagon ({10/2}) with two sets of overlapping vertices and edges.

The middle image is the uniform truncated cube; it is represented by a Schläfli symbol t{p,q,...}.

A complete bitruncation, called a birectification, reduces original faces to points.

Edge-truncation is a beveling, or chamfer for polyhedra, similar to cantellation, but retaining the original vertices, and replacing edges by hexagons.

In partial truncation, or alternation, half of the vertices and connecting edges are completely removed.