Facet of a polyhedron

Convex polyhedra

Prominent non-convex polyhedra include the star polyhedra. The regular star polyhedra, also known as the Kepler–Poinsot polyhedra, are constructible via stellation or faceting of regular convex polyhedra. Stellation is the process of extending the faces (within their planes) so that they meet. Faceting is the process of removing parts of a polyhedron to create new faces (or facets) without creating any new vertices. A facet of a polyhedron is any polygon whose corners are vertices of the polyhedron, and is not a face; for example, a polygon involving diagonals (face diagonals or space diagonals). The stellation and faceting are inverse or reciprocal processes: the dual of some stellation is a faceting of the dual to the original polyhedron. Other examples are the Chazelle polyhedron and toroidal polyhedra.