<div style="float:right; margin:0em 0em 1em 1em; border:1px solid silver; padding:0.5em; text-align:center;"> Stella octangula as a faceting of the cube In [geometry](https://bliptext.com/articles/geometry), **faceting** (also spelled **facetting**) is the process of removing parts of a [polygon](https://bliptext.com/articles/polygon), [polyhedron](https://bliptext.com/articles/polyhedron) or [polytope](https://bliptext.com/articles/polytope), without creating any new [vertices](https://bliptext.com/articles/vertex-geometry). New edges of a faceted polyhedron may be created along [face diagonals](https://bliptext.com/articles/face-diagonal) or internal [space diagonals](https://bliptext.com/articles/space-diagonal). A faceted polyhedron will have two faces on each edge and creates new polyhedra or compounds of polyhedra. Faceting is the reciprocal or [dual](https://bliptext.com/articles/duality-mathematics) process to [stellation](https://bliptext.com/articles/stellation). For every stellation of some [convex polytope](https://bliptext.com/articles/convex-polytope), there exists a dual faceting of the [dual polytope](https://bliptext.com/articles/dual-polytope). # [undefined | upload.wikimedia.org/wikipedia/commons/e/ed/CubeAndStel.svg]

Faceted polygons

For example, a regular pentagon has one symmetry faceting, the pentagram, and the regular hexagon has two symmetric facetings, one as a polygon, and one as a compound of two triangles.

Faceted polyhedra

The regular icosahedron can be faceted into three regular Kepler–Poinsot polyhedra: small stellated dodecahedron, great dodecahedron, and great icosahedron. They all have 30 edges. 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.

History

Faceting has not been studied as extensively as stellation.