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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 Tetrahedron.svg?width=300.
• Uniform_polyhedron wikiPageExternalLink 2254.
• Uniform_polyhedron wikiPageExternalLink 401.full.pdf.
• 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 wikiPageLength "59584".
• Uniform_polyhedron wikiPageOutDegree "782".
• Uniform_polyhedron wikiPageRevisionID "676635744".
• Uniform_polyhedron wikiPageWikiLink Alternation_(geometry).
• Uniform_polyhedron wikiPageWikiLink Antiprism.
• Uniform_polyhedron wikiPageWikiLink Archimedean_solid.
• Uniform_polyhedron wikiPageWikiLink Archimedes.
• Uniform_polyhedron wikiPageWikiLink Bipyramid.
• Uniform_polyhedron wikiPageWikiLink Cantellation_(geometry).
• Uniform_polyhedron wikiPageWikiLink Catalan_solid.
• Uniform_polyhedron wikiPageWikiLink Category:Uniform_polyhedra.
• Uniform_polyhedron wikiPageWikiLink Congruence_(geometry).
• Uniform_polyhedron wikiPageWikiLink Convex_polyhedron.
• Uniform_polyhedron wikiPageWikiLink Convex_polytope.
• Uniform_polyhedron wikiPageWikiLink Coxeter-Dynkin_diagram.
• Uniform_polyhedron wikiPageWikiLink Coxeter_diagram.
• Uniform_polyhedron wikiPageWikiLink Coxeter_group.
• Uniform_polyhedron wikiPageWikiLink Coxeter–Dynkin_diagram.
• Uniform_polyhedron wikiPageWikiLink Cube.
• Uniform_polyhedron wikiPageWikiLink Cuboctahedron.
• Uniform_polyhedron wikiPageWikiLink Decagon.
• Uniform_polyhedron wikiPageWikiLink Decagonal_bipyramid.
• Uniform_polyhedron wikiPageWikiLink Decagonal_dihedron.
• Uniform_polyhedron wikiPageWikiLink Decagonal_prism.
• Uniform_polyhedron wikiPageWikiLink Digon.
• Uniform_polyhedron wikiPageWikiLink Digonal_antiprism.
• Uniform_polyhedron wikiPageWikiLink Digonal_dihedron.
• Uniform_polyhedron wikiPageWikiLink Digonal_hosohedron.
• Uniform_polyhedron wikiPageWikiLink Dihedral_group.
• Uniform_polyhedron wikiPageWikiLink Dihedral_symmetry.
• Uniform_polyhedron wikiPageWikiLink Dihedron.
• Uniform_polyhedron wikiPageWikiLink Disdyakis_dodecahedron.
• Uniform_polyhedron wikiPageWikiLink Disdyakis_triacontahedron.
• Uniform_polyhedron wikiPageWikiLink Dodecagon.
• Uniform_polyhedron wikiPageWikiLink Dodecagonal_bipyramid.
• Uniform_polyhedron wikiPageWikiLink Dodecagonal_dihedron.
• Uniform_polyhedron wikiPageWikiLink Dodecagonal_prism.
• Uniform_polyhedron wikiPageWikiLink Dodecahedron.
• Uniform_polyhedron wikiPageWikiLink Dual_polyhedra.
• Uniform_polyhedron wikiPageWikiLink Dual_polyhedron.
• Uniform_polyhedron wikiPageWikiLink Edmond_Bonan.
• Uniform_polyhedron wikiPageWikiLink Edmund_Hess.
• Uniform_polyhedron wikiPageWikiLink Euclid.
• Uniform_polyhedron wikiPageWikiLink Expansion_(geometry).
• Uniform_polyhedron wikiPageWikiLink Face-transitive.
• Uniform_polyhedron wikiPageWikiLink Face_(geometry).
• Uniform_polyhedron wikiPageWikiLink File:Disdyakisdodecahedron.jpg.
• Uniform_polyhedron wikiPageWikiLink Great_disnub_dirhombidodecahedron.
• Uniform_polyhedron wikiPageWikiLink Group_action.
• Uniform_polyhedron wikiPageWikiLink H.C._Longuet-Higgins.
• Uniform_polyhedron wikiPageWikiLink H._Christopher_Longuet-Higgins.
• Uniform_polyhedron wikiPageWikiLink Harold_Scott_MacDonald_Coxeter.
• Uniform_polyhedron wikiPageWikiLink Hexagon.
• Uniform_polyhedron wikiPageWikiLink Hexagonal_antiprism.
• Uniform_polyhedron wikiPageWikiLink Hexagonal_bipyramid.
• Uniform_polyhedron wikiPageWikiLink Hexagonal_dihedron.
• Uniform_polyhedron wikiPageWikiLink Hexagonal_hosohedron.
• Uniform_polyhedron wikiPageWikiLink Hexagonal_prism.
• Uniform_polyhedron wikiPageWikiLink Hosohedron.
• Uniform_polyhedron wikiPageWikiLink Icosahedral_symmetry.
• Uniform_polyhedron wikiPageWikiLink Icosahedron.
• Uniform_polyhedron wikiPageWikiLink Icosidodecahedron.
• Uniform_polyhedron wikiPageWikiLink Infinite_set.
• Uniform_polyhedron wikiPageWikiLink Isogonal_figure.
• Uniform_polyhedron wikiPageWikiLink Isohedral_figure.
• Uniform_polyhedron wikiPageWikiLink Isometry.
• Uniform_polyhedron wikiPageWikiLink J._C._P._Miller.
• Uniform_polyhedron wikiPageWikiLink Johannes_Kepler.
• Uniform_polyhedron wikiPageWikiLink Kepler–Poinsot_polyhedra.
• Uniform_polyhedron wikiPageWikiLink Kepler–Poinsot_polyhedron.
• Uniform_polyhedron wikiPageWikiLink List_of_Johnson_solids.
• Uniform_polyhedron wikiPageWikiLink List_of_Wenninger_polyhedron_models.
• Uniform_polyhedron wikiPageWikiLink List_of_uniform_polyhedra.
• Uniform_polyhedron wikiPageWikiLink List_of_uniform_polyhedra_by_Schwarz_triangle.
• Uniform_polyhedron wikiPageWikiLink List_of_uniform_polyhedra_by_Wythoff_symbol.
• Uniform_polyhedron wikiPageWikiLink List_of_uniform_polyhedra_by_vertex_figure.
• Uniform_polyhedron wikiPageWikiLink Louis_Poinsot.
• Uniform_polyhedron wikiPageWikiLink Magnus_Wenninger.
• Uniform_polyhedron wikiPageWikiLink Mathematica.
• Uniform_polyhedron wikiPageWikiLink Michael_S._Longuet-Higgins.
• Uniform_polyhedron wikiPageWikiLink Norman_Johnson_(mathematician).
• Uniform_polyhedron wikiPageWikiLink Octagon.
• Uniform_polyhedron wikiPageWikiLink Octagonal_bipyramid.
• Uniform_polyhedron wikiPageWikiLink Octagonal_dihedron.

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