Convex core

When the facets of a polytope intersect one another, the facet hyperplanes may partition off a hypervolume at the center of the polytope in the shape of another polytope. This second polytope is the convex core, or kernel, of the original polytope. Particularly complicated polytopes may have many such partitions in them, but only the one at the center is the convex core.

For example, the convex core of a small stellated dodecahedron is a dodecahedron. Conveniently, its edges can be seen without having to dive into the bulk of the polytope, but this is not always the case.

The convex core of a convex polytope is the same polytope. Hence the concept is usually only applied to self-intersecting polytopes.

The convex core usually has the same symmetry and dimension as the original polytope.

When facets go through the center of the polytope, such as in the octahemioctahedron, it has no convex core.