Cantellation (geometry)

Cantellation (geometry)

In geometry, a cantellation is an operation in any dimension that cuts a regular polytope edges and vertices, creating a new facet in place of each edge and vertex. The operation also applies to regular tilings and honeycombs.

It is represented by an extended Schläfli symbol t0,2{p,q,...}.

For polyhedra, a cantellation operation offers a direct sequence from a regular polyhedron and its dual.

This operation (for polyhedra and tilings) is also called expansion by Alicia Boole Stott, as imagined by taking the faces of the regular form moving them away from the center and filling in new faces in the gaps for each opened vertex and edge.

Example cantellation sequence between a cube and octahedron

For higher dimensional polytopes, a cantellation offers a direct sequence from a regular polytope and its rectified form.

See also

* uniform polyhedron
* uniform polychoron
* Rectification (geometry)


Wikimedia Foundation. 2010.

Игры ⚽ Поможем сделать НИР

Look at other dictionaries:

  • Alternation (geometry) — In geometry, an alternation (also called partial truncation ) is an operation on a polyhedron or tiling that fully truncates alternate vertices. Only even sided polyhedra can be alternated, for example the zonohedra. Every 2n sided face becomes n …   Wikipedia

  • Expansion (geometry) — [ dodecahedron creates a rhombicosidodecahedron and a reverse expansion creates an icosahedron.] In geometry, expansion is a polytope operation where facets are separated and moved radially apart, and new facets are formed at separated elements… …   Wikipedia

  • Symbole de Schläfli — En mathématiques, le symbole de Schläfli est une notation de la forme {p,q,r, …} qui permet de définir les polyèdres réguliers et les tessellations. Cette notation donne un résumé de certaines propriétés importantes d un polytope régulier… …   Wikipédia en Français

  • Runcination — In geometry, a runcination is an operation that cuts a regular polytope (or honeycomb) simultaneously along the faces, edges and vertices, creating new facets in place of the original face, edge, and vertex centers.It is a higher order truncation …   Wikipedia

  • List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia

  • Omnitruncation — In geometry, an omnitruncation is an operation applied to a regular polytope (or honeycomb) in a Wythoff construction that creates a maximum number of facets. It is represented in a Coxeter–Dynkin diagram with all nodes ringed. It is a shortcut… …   Wikipedia

  • Small complex rhombicosidodecahedron — Type Uniform star polyhedron Elements F = 62, E = 120 (60x2) V = 20 (χ = 38) Faces by sides 20{3}+12{5/2}+30{4} …   Wikipedia

  • Uniform polytope — A uniform polytope is a vertex transitive polytope made from uniform polytope facets. A uniform polytope must also have only regular polygon faces.Uniformity is a generalization of the older category semiregular, but also includes the regular… …   Wikipedia

  • Uniform tiling — In geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex uniform.Uniform tilings can exist in both the Euclidean plane and hyperbolic plane. Uniform tilings are related to the… …   Wikipedia

  • Cuboctahedron — (Click here for rotating model) Type Archimedean solid Uniform polyhedron Elements F = 14, E = 24, V = 12 (χ = 2) Faces by sides 8{3}+6{4} …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”