Stellation

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Note how the smaller stellations of the enneagon are contained within the larger ones, and how the final stellation reaches to the ends of the extended edges.
{9/3} is a compound of 3 triangles.

At its simplest, stellation is the process of extending the facets of a polytope until they meet, forming a new polytope of the same rank as the original.

The "stellation diagram" for the facet of a polytope is formed by finding all the intersections of the facet's hyperplane with other facets' hyperplanes. The furthest extents of the stellation diagram form the facet of the "final stellation" of the polytope.

A stellation may be a compound, even if the original polytope isn't. If an isotopic polytope has a convex core, it is a stellation of the core.

The dual of the stellation of a polytope will always be a faceting of the dual of the polytope, and vice versa.

Some stellations of the icosahedron, and their faces (stellation diagrams)
Icosahedron Small triambic icosahedron Crennell number 4 stellation
of the icosahedron
Great icosahedron