Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Semiregular_polyhedron> ?p ?o }
- Semiregular_polyhedron abstract "The term semiregular polyhedron (or semiregular polytope) is used variously by different authors.In its original definition, it is a polyhedron with regular faces and a symmetry group which is transitive on its vertices, which is more commonly referred to today as a uniform polyhedron (this follows from Thorold Gosset's 1900 definition of the more general semiregular polytope). These polyhedra include:The thirteen Archimedean solids.An infinite series of convex prisms.An infinite series of convex antiprisms (their semiregular nature was first observed by Kepler).These semiregular solids can be fully specified by a vertex configuration, a listing of the faces by number of sides in order as they occur around a vertex. For example, 3.5.3.5, represents the icosidodecahedron which alternates two triangles and two pentagons around each vertex. 3.3.3.5 in contrast is a pentagonal antiprism. These polyhedra are sometimes described as vertex-transitive.Since Gosset, other authors have used the term semiregular in different ways in relation to higher dimensional polytopes. E. L. Elte provided a definition which Coxeter found too artificial. Coxeter himself dubbed Gosset's figures uniform, with only a quite restricted subset classified as semiregular.Yet others have taken the opposite path, categorising more polyhedra as semiregular. These include:Three sets of star polyhedra which meet Gosset's definition, analogous to the three convex sets listed above.The duals of the above semiregular solids, arguing that since the dual polyhedra share the same symmetries as the originals, they too should be regarded as semiregular. These duals include the Catalan solids, the convex dipyramids and antidipyramids or trapezohedra, and their nonconvex analogues.A further source of confusion lies in the way that the Archimedean solids are defined, again with different interpretations appearing.Gosset's definition of semiregular includes figures of higher symmetry, the regular and quasiregular polyhedra. Some later authors prefer to say that these are not semiregular, because they are more regular than that - the uniform polyhedra are then said to include the regular, quasiregular and semiregular ones. This naming system works well, and reconciles many (but by no means all) of the confusions.In practice even the most eminent authorities can get themselves confused, defining a given set of polyhedra as semiregular and/or Archimedean, and then assuming (or even stating) a different set in subsequent discussions. Assuming that one's stated definition applies only to convex polyhedra is probably the commonest failing. Coxeter, Cromwell and Cundy & Rollett are all guilty of such slips.".
- Semiregular_polyhedron thumbnail Truncated_tetrahedron.png?width=300.
- Semiregular_polyhedron wikiPageExternalLink s084300.htm.
- Semiregular_polyhedron wikiPageExternalLink semiregularpolyhedron.html.
- Semiregular_polyhedron wikiPageExternalLink semi-regular_polyhedron.html.
- Semiregular_polyhedron wikiPageExternalLink archimedean-info.html.
- Semiregular_polyhedron wikiPageID "1548894".
- Semiregular_polyhedron wikiPageLength "8016".
- Semiregular_polyhedron wikiPageOutDegree "65".
- Semiregular_polyhedron wikiPageRevisionID "674404507".
- Semiregular_polyhedron wikiPageWikiLink Antiprism.
- Semiregular_polyhedron wikiPageWikiLink Archimedean_solid.
- Semiregular_polyhedron wikiPageWikiLink Bipyramid.
- Semiregular_polyhedron wikiPageWikiLink Catalan_solid.
- Semiregular_polyhedron wikiPageWikiLink Category:Polyhedra.
- Semiregular_polyhedron wikiPageWikiLink Convex_set.
- Semiregular_polyhedron wikiPageWikiLink Dual_polyhedron.
- Semiregular_polyhedron wikiPageWikiLink Emanuel_Lodewijk_Elte.
- Semiregular_polyhedron wikiPageWikiLink Eric_W._Weisstein.
- Semiregular_polyhedron wikiPageWikiLink Group_action.
- Semiregular_polyhedron wikiPageWikiLink Icosidodecahedron.
- Semiregular_polyhedron wikiPageWikiLink Isogonal_figure.
- Semiregular_polyhedron wikiPageWikiLink Johannes_Kepler.
- Semiregular_polyhedron wikiPageWikiLink Pentagon.
- Semiregular_polyhedron wikiPageWikiLink Pentagonal_antiprism.
- Semiregular_polyhedron wikiPageWikiLink Platonic_solid.
- Semiregular_polyhedron wikiPageWikiLink Polyhedron.
- Semiregular_polyhedron wikiPageWikiLink Polytope.
- Semiregular_polyhedron wikiPageWikiLink Prism_(geometry).
- Semiregular_polyhedron wikiPageWikiLink Quasiregular_polyhedron.
- Semiregular_polyhedron wikiPageWikiLink Regular_polygon.
- Semiregular_polyhedron wikiPageWikiLink Regular_polyhedron.
- Semiregular_polyhedron wikiPageWikiLink Robert_Williams_(geometer).
- Semiregular_polyhedron wikiPageWikiLink Semiregular_polytope.
- Semiregular_polyhedron wikiPageWikiLink Star_polyhedron.
- Semiregular_polyhedron wikiPageWikiLink Symmetry_group.
- Semiregular_polyhedron wikiPageWikiLink Thorold_Gosset.
- Semiregular_polyhedron wikiPageWikiLink Trapezohedron.
- Semiregular_polyhedron wikiPageWikiLink Triangle.
- Semiregular_polyhedron wikiPageWikiLink Uniform_polyhedron.
- Semiregular_polyhedron wikiPageWikiLink Vertex_(geometry).
- Semiregular_polyhedron wikiPageWikiLink Vertex_configuration.
- Semiregular_polyhedron wikiPageWikiLink Wythoff_construction.
- Semiregular_polyhedron wikiPageWikiLink File:Cuboctahedron.png.
- Semiregular_polyhedron wikiPageWikiLink File:Great_rhombicosidodecahedron.png.
- Semiregular_polyhedron wikiPageWikiLink File:Great_rhombicuboctahedron.png.
- Semiregular_polyhedron wikiPageWikiLink File:Hexagonal_antiprism.png.
- Semiregular_polyhedron wikiPageWikiLink File:Hexagonal_prism.png.
- Semiregular_polyhedron wikiPageWikiLink File:Icosidodecahedron.png.
- Semiregular_polyhedron wikiPageWikiLink File:Pentagonal_antiprism.png.
- Semiregular_polyhedron wikiPageWikiLink File:Pentagonal_prism.png.
- Semiregular_polyhedron wikiPageWikiLink File:Prism_7.png.
- Semiregular_polyhedron wikiPageWikiLink File:Small_rhombicosidodecahedron.png.
- Semiregular_polyhedron wikiPageWikiLink File:Small_rhombicuboctahedron.png.
- Semiregular_polyhedron wikiPageWikiLink File:Snub_dodecahedron_ccw.png.
- Semiregular_polyhedron wikiPageWikiLink File:Snub_hexahedron.png.
- Semiregular_polyhedron wikiPageWikiLink File:Square_antiprism.png.
- Semiregular_polyhedron wikiPageWikiLink File:Triangular_prism.png.
- Semiregular_polyhedron wikiPageWikiLink File:Truncated_dodecahedron.png.
- Semiregular_polyhedron wikiPageWikiLink File:Truncated_hexahedron.png.
- Semiregular_polyhedron wikiPageWikiLink File:Truncated_icosahedron.png.
- Semiregular_polyhedron wikiPageWikiLink File:Truncated_octahedron.png.
- Semiregular_polyhedron wikiPageWikiLink File:Truncated_tetrahedron.png.
- Semiregular_polyhedron wikiPageWikiLinkText "Convex semiregular".
- Semiregular_polyhedron wikiPageWikiLinkText "Polyhedra".
- Semiregular_polyhedron wikiPageWikiLinkText "Semi-regular".
- Semiregular_polyhedron wikiPageWikiLinkText "Semiregular polyhedra".
- Semiregular_polyhedron wikiPageWikiLinkText "Semiregular polyhedron".
- Semiregular_polyhedron wikiPageWikiLinkText "Semiregular".
- Semiregular_polyhedron wikiPageWikiLinkText "convex semiregular".
- Semiregular_polyhedron wikiPageWikiLinkText "semi-regular".
- Semiregular_polyhedron wikiPageWikiLinkText "semiregular polyhedra".
- Semiregular_polyhedron wikiPageWikiLinkText "semiregular polyhedron".
- Semiregular_polyhedron wikiPageWikiLinkText "semiregular".
- Semiregular_polyhedron title "Semiregular polyhedron".
- Semiregular_polyhedron urlname "SemiregularPolyhedron".
- Semiregular_polyhedron wikiPageUsesTemplate Template:MathWorld.
- Semiregular_polyhedron subject Category:Polyhedra.
- Semiregular_polyhedron hypernym Polyhedron.
- Semiregular_polyhedron type Polytope.
- Semiregular_polyhedron comment "The term semiregular polyhedron (or semiregular polytope) is used variously by different authors.In its original definition, it is a polyhedron with regular faces and a symmetry group which is transitive on its vertices, which is more commonly referred to today as a uniform polyhedron (this follows from Thorold Gosset's 1900 definition of the more general semiregular polytope).".
- Semiregular_polyhedron label "Semiregular polyhedron".
- Semiregular_polyhedron sameAs Q2311217.
- Semiregular_polyhedron sameAs Паўправільны_шматграннік.
- Semiregular_polyhedron sameAs Ημικανονικό_πολύεδρο.
- Semiregular_polyhedron sameAs Duonregula_pluredro.
- Semiregular_polyhedron sameAs Poliedro_semirregular.
- Semiregular_polyhedron sameAs Poliedro_erdierregular.
- Semiregular_polyhedron sameAs Polyèdre_semi-régulier.
- Semiregular_polyhedron sameAs פאון_משוכלל_למחצה.
- Semiregular_polyhedron sameAs 반정다면체.
- Semiregular_polyhedron sameAs Pustaisyklingis_briaunainis.
- Semiregular_polyhedron sameAs Halfregelmatig_veelvlak.
- Semiregular_polyhedron sameAs m.059j_w.
- Semiregular_polyhedron sameAs Полуправильный_многогранник.
- Semiregular_polyhedron sameAs Polpravilni_polieder.
- Semiregular_polyhedron sameAs Напівправильний_многогранник.
- Semiregular_polyhedron sameAs Q2311217.
- Semiregular_polyhedron sameAs 半正多面體.
- Semiregular_polyhedron wasDerivedFrom Semiregular_polyhedron?oldid=674404507.