Stella octangula as a facetting of the cube
In geometry, facetting (also spelled 'faceting') is the process of removing parts of a polygon, polyhedron or polytope, without creating any new vertices.
Facetting is the reciprocal or dual process to stellation. For every stellation of some convex polytope, there exists a dual facetting of the dual polytope.
For example the stellated dodecahedron and great icosahedron'' are two facettings of the icosahedron:
Facetting has not been studied as extensively as stellation.
- Bertrand, J. Note sur la théorie des polyèdres réguliers, Comptes rendus des séances de l'Académie des Sciences, 46 (1858), pp. 79-82.
- Bridge, N.J. Facetting the dodecahedron, Acta crystallographica A30 (1974), pp. 548-552.
- Inchbald, G. Facetting diagrams, The mathematical gazette, 90 (2006), pp. 253-261.