Expansion (geometry)

In geometry, expansion is a polytope operation where facets are separated and moved radially apart, and new facets are formed at separated elements (vertices, edges, etc.).

Equivalently this operation can be imagined by keeping facets in the same position but reducing their size.

The expansion operation is symmetric with respect to a regular polytope and its dual.

In a Wythoff construction, an expansion is generated by reflections from the first and last mirrors.

By dimension: The general operator for expansion of a regular n-polytope is t0,n-1{p,q,r,...}.

An example of expanding pentagon into a decagon by moving edges away from the center and inserting new edges in the gaps. The expansion is uniform if all the edges are the same length.
Animation showing an expanded cube (and octahedron )