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Expansion (geometry)

Not to be confused with enlargement (geometry).
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)

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 of a regular convex polytope creates a uniform convex polytope.

For polyhedra, an expanded polyhedron has all the faces of the original polyhedron, all the faces of the dual polyhedron, and new square faces in place of the original edges.

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