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This list includes these: all 75 nonprismatic uniform polyhedra; a few representatives of the infinite sets of prisms and antiprisms; one degenerate polyhedron, Skilling's figure with overlapping edges. It was proven in Sopov (1970) that there are only 75 uniform polyhedra other than the infinite families of prisms and antiprisms. John Skilling ...
A polytope is a geometric object with flat sides, which exists in any general number of dimensions. The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples.
In 1974, Magnus Wenninger published his book Polyhedron models, which lists all 75 nonprismatic uniform polyhedra, with many previously unpublished names given to them by Norman Johnson. Skilling (1975) independently proved the completeness and showed that if the definition of uniform polyhedron is relaxed to allow edges to coincide then there ...
name of polyhedron; alternate names (in brackets) Wythoff symbol; Numbering systems: W - number used by Wenninger in polyhedra models, U - uniform indexing, K - Kaleido indexing, C - numbering used in Coxeter et al. 'Uniform Polyhedra'. Number of vertices V, edges E, Faces F and number of faces by type. Euler characteristic χ = V - E + F
All of these classes are convex polyhedrons. A convex polyhedron is a polyhedron that forms a convex set as a solid. That being said, it is a three-dimensional solid whose every line segment connects two of its points lies its interior or on its boundary ; none of its faces are coplanar (they do not share the same plane) and none of its edges ...
This category lists terms related to Polyhedra, for individual polyhedra see the sub categories: . Category:Uniform polyhedra includes subcategories below AND 53 nonconvex forms:
All five have C 2 ×S 5 symmetry but can only be realised with half the symmetry, that is C 2 ×A 5 or icosahedral symmetry. [9] [10] [11] They are all topologically equivalent to toroids. Their construction, by arranging n faces around each vertex, can be repeated indefinitely as tilings of the hyperbolic plane. In the diagrams below, the ...
In geometry, a polyhedron is a solid in three dimensions with flat faces and straight edges. Every edge has exactly two faces, and every vertex is surrounded by alternating faces and edges.