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- Uniform_polyhedron abstract "A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive(transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational symmetry. Uniform polyhedra may be regular (if also face and edge transitive), quasi-regular (if edge transitive but not face transitive) or semi-regular (if neither edge nor face transitive). The faces and vertices need not be convex, so many of the uniform polyhedra are also star polyhedra.Excluding the infinite sets, there are 75 uniform polyhedra (or 76 if edges are allowed to coincide). Convex 5 Platonic solids – regular convex polyhedra 13 Archimedean solids – 2 quasiregular and 11 semiregular convex polyhedra Star 4 Kepler–Poinsot polyhedra – regular nonconvex polyhedra 53 uniform star polyhedra – 5 quasiregular and 48 semiregular 1 star polyhedron found by John Skilling with pairs of edges that coincide, called the great disnub dirhombidodecahedron (Skilling's figure).There are also two infinite sets of uniform prisms and antiprisms, including convex and star forms.Dual polyhedra to uniform polyhedra are face-transitive (isohedral) and have regular vertex figures, and are generally classified in parallel with their dual (uniform) polyhedron. The dual of a regular polyhedron is regular, while the dual of an Archimedean solid is a Catalan solid.The concept of uniform polyhedron is a special case of the concept of uniform polytope, which also applies to shapes in higher-dimensional (or lower-dimensional) space.".
- Uniform_polyhedron thumbnail Wythoffian_construction_diagram.png?width=300.
- Uniform_polyhedron wikiPageExternalLink 2254.
- Uniform_polyhedron wikiPageExternalLink uniform-info.html.
- Uniform_polyhedron wikiPageExternalLink bibperm?q1=ABN8316.0001.001.
- Uniform_polyhedron wikiPageExternalLink ~rl.
- Uniform_polyhedron wikiPageExternalLink uniform.pdf.
- Uniform_polyhedron wikiPageExternalLink kaleido.
- Uniform_polyhedron wikiPageExternalLink dual.html.
- Uniform_polyhedron wikiPageExternalLink poly.html.
- Uniform_polyhedron wikiPageExternalLink unipoly.
- Uniform_polyhedron wikiPageExternalLink unipoly.
- Uniform_polyhedron wikiPageExternalLink ?p=baeede46029e489f9df9a31526cd8f6&pi=2.
- Uniform_polyhedron wikiPageExternalLink &var2=3.
- Uniform_polyhedron wikiPageID "2537223".
- Uniform_polyhedron wikiPageRevisionID "605992794".
- Uniform_polyhedron hasPhotoCollection Uniform_polyhedron.
- Uniform_polyhedron title "Uniform Polyhedron".
- Uniform_polyhedron urlname "UniformPolyhedron".
- Uniform_polyhedron subject Category:Uniform_polyhedra.
- Uniform_polyhedron comment "A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive(transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational symmetry.".
- Uniform_polyhedron label "Poliedro uniforme".
- Uniform_polyhedron label "Polyèdre uniforme".
- Uniform_polyhedron label "Uniform polyhedron".
- Uniform_polyhedron label "一様多面体".
- Uniform_polyhedron label "均勻多面體".
- Uniform_polyhedron sameAs Poliedro_uniforme.
- Uniform_polyhedron sameAs Polyèdre_uniforme.
- Uniform_polyhedron sameAs Poliedro_uniforme.
- Uniform_polyhedron sameAs 一様多面体.
- Uniform_polyhedron sameAs 고른_다면체.
- Uniform_polyhedron sameAs m.07lpqy.
- Uniform_polyhedron sameAs Q2471563.
- Uniform_polyhedron sameAs Q2471563.
- Uniform_polyhedron wasDerivedFrom Uniform_polyhedron?oldid=605992794.
- Uniform_polyhedron depiction Wythoffian_construction_diagram.png.
- Uniform_polyhedron isPrimaryTopicOf Uniform_polyhedron.
