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nonconvex space

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  • Nonconvex uniform polyhedron — In geometry, a nonconvex uniform polyhedron, or uniform star polyhedron, is a self intersecting uniform polyhedron. Each can contain either star polygon faces, star polygon vertex figures or both.The complete set of 57 nonprismatic uniform star… …   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

  • List of regular polytopes — This page lists the regular polytopes in Euclidean, spherical and hyperbolic spaces.The Schläfli symbol notation describes every regular polytope, and is used widely below as a compact reference name for each.The regular polytopes are grouped by… …   Wikipedia

  • Uniform star polyhedron — A display of uniform polyhedra at the Science Museum in London …   Wikipedia

  • Uniform polychoron — In geometry, a uniform polychoron (plural: uniform polychora) is a polychoron or 4 polytope which is vertex transitive and whose cells are uniform polyhedra.This article contains the complete list of 64 non prismatic convex uniform polychora, and …   Wikipedia

  • Schläfli symbol — In mathematics, the Schläfli symbol is a notation of the form {p,q,r,...} that defines regular polytopes and tessellations.The Schläfli symbol is named after the 19th century mathematician Ludwig Schläfli who made important contributions in… …   Wikipedia

  • Polychoron — In geometry, a four dimensional polytope is sometimes called a polychoron (plural: polychora), from the Greek root poly , meaning many , and choros meaning room or space .It is also called a 4 polytope or polyhedroid. The two dimensional analogue …   Wikipedia

  • Dodecadodecahedron — Type Uniform star polyhedron Elements F = 24, E = 60 V = 30 (χ = −6) Faces by sides 12{5}+12{5/2} Wythoff symbol …   Wikipedia

  • Convexity in economics — Economics …   Wikipedia

  • Dodecahedron — Regular Dodecahedron (Click here for rotating model) Type Platonic solid Elements F = 12, E = 30 V = 20 (χ = 2) Faces by sides 12{5} …   Wikipedia

  • Vertex figure — In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off. Definitions theme and variationsTake some vertex of a polyhedron. Mark a point somewhere along each connected edge. Draw …   Wikipedia

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