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For other uses, see Facetting (disambiguation).

Stella octangula as a faceting of the cube

In geometry, faceting (also spelled facetting) is the process of removing parts of a polygon, polyhedron or polytope, without creating any new vertices.

Faceting is the reciprocal or dual process to stellation. For every stellation of some convex polytope, there exists a dual faceting of the dual polytope.

For example the small stellated dodecahedron and great icosahedron are two facetings of the icosahedron:

icosahedron small stellated dodecahedron great icosahedron
Icosahedron.png Small stellated dodecahedron.png Great icosahedron.png


Faceting 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.

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