Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Wythoff_symbol> ?p ?o }
- Wythoff_symbol abstract "In geometry, the Wythoff symbol was first used by Coxeter, Longuet-Higgins and Miller in their enumeration of the uniform polyhedra. It represents a construction by way of Wythoff's construction applied to Schwarz triangles.A Schwarz triangle is a triangle that, with its own reflections in its edges, covers the sphere or the plane a finite number of times. The usual representation for the triangle is three numbers – integers or fractions – such that π/x is the angle at one vertex. For example, the triangle (2 3 4) represents the symmetry of a cube, while (5/2 5/2 5/2) is the face of an icosahedron.Wythoff's construction in three dimensions consists of choosing a point in the triangle whose distance from each of the sides, if nonzero, is equal, and dropping perpendiculars to each of the edges.Each edge of the triangle is named for the opposite angle; thus an edge opposite a right angle is designated '2'. The symbol then corresponds to a representation of off | on. Each of the numbers p in the symbol becomes a polygon pn, where n is the number of other edges that appear before the bar. So in 3 | 4 2 the vertex – a point, being here a degenerate polygon with 3×0 sides – lies on the π/3 corner of the triangle, and the altitude from that corner can be considered as forming half of the boundary between a square (having 4×1 sides) and a digon (having 2×1 sides) of zero area.The special case of the snub figures is done by using the symbol | p q r, which would normally put the vertex at the centre of the sphere. The faces of a snub alternate as p 3 q 3 r 3. This gives an antiprism when q=r=2.Each symbol represents one uniform polyhedron or tiling, although the same tiling/polyhedron can have different Wythoff symbols from different symmetry generators. For example, the regular cube can be represented by 3 | 4 2 with Oh symmetry, and 2 4 | 2 as a square prism with 2 colors and D4h symmetry, as well as 2 2 2 | with 3 colors and D2h symmetry.It can be applied with a slight extension to all uniform polyhedra, but the construction methods do not lead to all uniform tilings in euclidean or hyperbolic space.".
- Wythoff_symbol thumbnail Wythoffian_construction_diagram.png?width=300.
- Wythoff_symbol wikiPageExternalLink HyperbolicTesselations.
- Wythoff_symbol wikiPageExternalLink index.html.
- Wythoff_symbol wikiPageExternalLink 26.html.
- Wythoff_symbol wikiPageExternalLink WythoffNotes.html.
- Wythoff_symbol wikiPageExternalLink entry.html?action=entryByConcept&id=2788&langcode=en.
- Wythoff_symbol wikiPageExternalLink wythoff.html.
- Wythoff_symbol wikiPageID "3691548".
- Wythoff_symbol wikiPageLength "58137".
- Wythoff_symbol wikiPageOutDegree "937".
- Wythoff_symbol wikiPageRevisionID "637443802".
- Wythoff_symbol wikiPageWikiLink 3-7_kisrhombille.
- Wythoff_symbol wikiPageWikiLink Alternated_octagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Alternated_order-4_hexagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Antiprism.
- Wythoff_symbol wikiPageWikiLink Cantic_octagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Cantic_order-4_hexagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Category:Mathematical_notation.
- Wythoff_symbol wikiPageWikiLink Category:Polyhedra.
- Wythoff_symbol wikiPageWikiLink Category:Polytopes.
- Wythoff_symbol wikiPageWikiLink Coxeter–Dynkin_diagram.
- Wythoff_symbol wikiPageWikiLink Cube.
- Wythoff_symbol wikiPageWikiLink Cuboctahedron.
- Wythoff_symbol wikiPageWikiLink Decagonal_bipyramid.
- Wythoff_symbol wikiPageWikiLink Decagonal_prism.
- Wythoff_symbol wikiPageWikiLink Digon.
- Wythoff_symbol wikiPageWikiLink Dihedral_group.
- Wythoff_symbol wikiPageWikiLink Dihedral_symmetry_in_three_dimensions.
- Wythoff_symbol wikiPageWikiLink Dihedron.
- Wythoff_symbol wikiPageWikiLink Ditrigonal_triapeirogonal_tiling.
- Wythoff_symbol wikiPageWikiLink Dodecadodecahedron.
- Wythoff_symbol wikiPageWikiLink Dodecagonal_bipyramid.
- Wythoff_symbol wikiPageWikiLink Dodecagonal_prism.
- Wythoff_symbol wikiPageWikiLink Dodecahedron.
- Wythoff_symbol wikiPageWikiLink Expansion_(geometry).
- Wythoff_symbol wikiPageWikiLink File:Hyperbolic_domains_642.png.
- Wythoff_symbol wikiPageWikiLink File:Order-3_heptakis_heptagonal_tiling.png.
- Wythoff_symbol wikiPageWikiLink Geometry.
- Wythoff_symbol wikiPageWikiLink Great_dirhombicosidodecahedron.
- Wythoff_symbol wikiPageWikiLink Great_dodecahedron.
- Wythoff_symbol wikiPageWikiLink Great_icosahedron.
- Wythoff_symbol wikiPageWikiLink Great_icosidodecahedron.
- Wythoff_symbol wikiPageWikiLink Great_snub_icosidodecahedron.
- Wythoff_symbol wikiPageWikiLink Great_stellated_dodecahedron.
- Wythoff_symbol wikiPageWikiLink Harold_Scott_MacDonald_Coxeter.
- Wythoff_symbol wikiPageWikiLink Heptaapeirogonal_tiling.
- Wythoff_symbol wikiPageWikiLink Heptagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Heptaoctagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Hexaapeirogonal_tiling.
- Wythoff_symbol wikiPageWikiLink Hexagonal_antiprism.
- Wythoff_symbol wikiPageWikiLink Hexagonal_bipyramid.
- Wythoff_symbol wikiPageWikiLink Hexagonal_prism.
- Wythoff_symbol wikiPageWikiLink Hexagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Hexaheptagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Hexaoctagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Hosohedron.
- Wythoff_symbol wikiPageWikiLink Hyperbolic_space.
- Wythoff_symbol wikiPageWikiLink Icosahedral_symmetry.
- Wythoff_symbol wikiPageWikiLink Icosahedron.
- Wythoff_symbol wikiPageWikiLink Icosidodecahedron.
- Wythoff_symbol wikiPageWikiLink Infinite-order_apeirogonal_tiling.
- Wythoff_symbol wikiPageWikiLink Infinite-order_heptagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Infinite-order_hexagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Infinite-order_octagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Infinite-order_pentagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Infinite-order_square_tiling.
- Wythoff_symbol wikiPageWikiLink Infinite-order_triangular_tiling.
- Wythoff_symbol wikiPageWikiLink Jeffrey_Weeks_(mathematician).
- Wythoff_symbol wikiPageWikiLink List_of_convex_uniform_tilings.
- Wythoff_symbol wikiPageWikiLink List_of_regular_polytopes_and_compounds.
- Wythoff_symbol wikiPageWikiLink List_of_uniform_polyhedra.
- Wythoff_symbol wikiPageWikiLink List_of_uniform_polyhedra_by_Schwarz_triangle.
- Wythoff_symbol wikiPageWikiLink Octaapeirogonal_tiling.
- Wythoff_symbol wikiPageWikiLink Octagonal_bipyramid.
- Wythoff_symbol wikiPageWikiLink Octagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Octahedral_symmetry.
- Wythoff_symbol wikiPageWikiLink Octahedron.
- Wythoff_symbol wikiPageWikiLink Order-3_apeirogonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-4_apeirogonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-4_heptagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-4_hexagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-4_octagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-4_pentagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-5_apeirogonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-5_heptagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-5_hexagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-5_octagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-5_pentagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-5_square_tiling.
- Wythoff_symbol wikiPageWikiLink Order-6_apeirogonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-6_heptagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-6_hexagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-6_octagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-6_pentagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-6_square_tiling.
- Wythoff_symbol wikiPageWikiLink Order-7_apeirogonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-7_heptagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-7_hexagonal_tiling.
- Wythoff_symbol wikiPageWikiLink Order-7_octagonal_tiling.