cantellation


cantellation
An operation in any dimension that cuts a regular polytope at its edges and vertices, creating a new facet in place of each edge and vertex.

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  • 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 …   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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • Cantellated tesseract — In geometry, the cantellated tesseract is a uniform polychora or 4 dimensional polytope bounded by 56 cells: 8 small rhombicuboctahedra, 16 octahedra, and 32 triangular prisms.ConstructionIn the process of cantellation, a polytopes faces are… …   Wikipedia


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