regular polytope
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Regular polytope — In mathematics, a regular polytope is a polytope whose symmetry is transitive on its flags, thus giving it the highest degree of symmetry. All its elements or j faces (for all 0≤ j ≤ n , where n is the dimension of the polytope) cells, faces and… … Wikipedia
Regular Polytopes (book) — Regular Polytopes is a mathematical geometry book written by Canadian mathematician H.S.M. Coxeter. Originally written in 1947, the book was updated and republished in 1963 and 1973.The book is a comprehensive survey of the geometry of regular… … Wikipedia
Polytope — Not to be confused with polytrope. In elementary geometry, a polytope is a geometric object with flat sides, which exists in any general number of dimensions. A polygon is a polytope in two dimensions, a polyhedron in three dimensions, and so on… … Wikipedia
Regular polyhedron — A regular polyhedron is a polyhedron whose faces are congruent (all alike) regular polygons which are assembled in the same way around each vertex. A regular polyhedron is highly symmetrical, being all of edge transitive, vertex transitive and… … Wikipedia
Regular 4-polytope — In geometry a regular 4 polytope can mean either a convex or nonconvex (intersecting) 4 polytope.See: * Convex regular 4 polytope There are six convex regular polychora. * Schläfli Hess polychoron There are ten star (self intersecting) regular… … Wikipedia
Polytope croisé — Octaèdre Octaèdre Type Polyèdre régulier Faces Triangle Éléments : · Faces · Arêtes · Sommets · Caractéristique 8 12 6 2 Faces par sommet 4 Sommets par face … Wikipédia en Français
Polytope — Un polytope en dimension 3 Le terme polytope admet plusieurs définitions au sein des mathématiques. Principalement car les usages diffèrent en quelques points selon les pays, mais l usage américain ayant tendance à s imposer, on se retrouve… … Wikipédia en Français
Regular polygon — A regular polygon is a polygon which is equiangular (all angles are congruent) and equilateral (all sides have the same length). Regular polygons may be convex or star.General propertiesThese properties apply to both convex and star regular… … 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
Cross-polytope — In geometry, a cross polytope,[1] orthoplex,[2] hyperoctahedron, or cocube is a regular, convex polytope that exists in any number of dimensions. The vertices of a cross polytope are all the permutations of (±1, 0, 0, …, 0). The cross polytope is … Wikipedia
Convex regular 4-polytope — The tesseract is one of 6 convex regular 4 polytopes In mathematics, a convex regular 4 polytope is a 4 dimensional polytope that is both regular and convex. These are the four dimensional analogs of the Platonic solids (in three dimensions) and… … Wikipedia
