New edges of a faceted polyhedron may be created along face diagonals or internal space diagonals. A faceted polyhedron will have two faces on each edge and creates new polyhedra or compounds of polyhedra.
The regular dodecahedron can be faceted into one regular Kepler-Poinsot polyhedron, three uniform star polyhedra, and three regular polyhedral compound. The uniform stars and compound of five cubes are constructed by face diagonals. The excavated dodecahedron is a facetting with star hexagon faces.
|Convex||Regular star||Uniform stars||Vertex-transitive|
|dodecahedron||great stellated dodecahedron||Small ditrigonal icosi-dodecahedron||Ditrigonal dodeca-dodecahedron||Great ditrigonal icosi-dodecahedron||Excavated dodecahedron|
Faceting has not been studied as extensively as stellation.