Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Schwarz_triangle> ?p ?o }
- Schwarz_triangle abstract "In geometry, a Schwarz triangle, named after Hermann Schwarz, is a spherical triangle that can be used to tile a sphere, possibly overlapping, through reflections in its edges. They were classified in (Schwarz 1873).These can be defined more generally as tessellations of the sphere, the Euclidean plane, or the hyperbolic plane. Each Schwarz triangle on a sphere defines a finite group, while on the Euclidean or hyperbolic plane they define an infinite group.A Schwarz triangle is represented by three rational numbers (p q r) each representing the angle at a vertex. The value n/d means the vertex angle is d/n of the half-circle. "2" means a right triangle. When these are whole numbers, the triangle is called a Möbius triangle, and corresponds to a non-overlapping tiling, and the symmetry group is called a triangle group. In the sphere there are 3 Möbius triangles plus one one-parameter family; in the plane there are three Möbius triangles, while in hyperbolic space there is a three-parameter family of Möbius triangles, and no exceptional objects.".
- Schwarz_triangle thumbnail Schwarz_triangle_on_sphere.png?width=300.
- Schwarz_triangle wikiPageExternalLink purl?GDZPPN002155206.
- Schwarz_triangle wikiPageExternalLink books?id=Olc5AAAAIAAJ&pg=PA132.
- Schwarz_triangle wikiPageID "2069325".
- Schwarz_triangle wikiPageLength "9263".
- Schwarz_triangle wikiPageOutDegree "60".
- Schwarz_triangle wikiPageRevisionID "664557079".
- Schwarz_triangle wikiPageWikiLink (2,3,7)_triangle_group.
- Schwarz_triangle wikiPageWikiLink 30-60-90.
- Schwarz_triangle wikiPageWikiLink 45-45-90.
- Schwarz_triangle wikiPageWikiLink Anthony_W._Knapp.
- Schwarz_triangle wikiPageWikiLink Bolza_surface.
- Schwarz_triangle wikiPageWikiLink Category:Polyhedra.
- Schwarz_triangle wikiPageWikiLink Category:Spherical_trigonometry.
- Schwarz_triangle wikiPageWikiLink Complete_graph.
- Schwarz_triangle wikiPageWikiLink Coxeter.
- Schwarz_triangle wikiPageWikiLink Coxeter-Dynkin_diagram.
- Schwarz_triangle wikiPageWikiLink Coxeter_group.
- Schwarz_triangle wikiPageWikiLink Coxeter–Dynkin_diagram.
- Schwarz_triangle wikiPageWikiLink Crelles_Journal.
- Schwarz_triangle wikiPageWikiLink Density_(polytope).
- Schwarz_triangle wikiPageWikiLink Dihedral_group.
- Schwarz_triangle wikiPageWikiLink Dihedral_symmetry.
- Schwarz_triangle wikiPageWikiLink Equilateral_triangle.
- Schwarz_triangle wikiPageWikiLink Exceptional_object.
- Schwarz_triangle wikiPageWikiLink File:Order-3_heptakis_heptagonal_tiling.png.
- Schwarz_triangle wikiPageWikiLink Finite_group.
- Schwarz_triangle wikiPageWikiLink Geometry.
- Schwarz_triangle wikiPageWikiLink Goursat_tetrahedron.
- Schwarz_triangle wikiPageWikiLink Harold_Scott_MacDonald_Coxeter.
- Schwarz_triangle wikiPageWikiLink Hermann_Schwarz.
- Schwarz_triangle wikiPageWikiLink Hurwitz_group.
- Schwarz_triangle wikiPageWikiLink Hurwitzs_automorphisms_theorem.
- Schwarz_triangle wikiPageWikiLink Icosahedral_symmetry.
- Schwarz_triangle wikiPageWikiLink Journal_für_die_reine_und_angewandte_Mathematik.
- Schwarz_triangle wikiPageWikiLink Klein_quartic.
- Schwarz_triangle wikiPageWikiLink List_of_regular_polytopes_and_compounds.
- Schwarz_triangle wikiPageWikiLink List_of_uniform_polyhedra_by_Schwarz_triangle.
- Schwarz_triangle wikiPageWikiLink Nonconvex_uniform_polyhedron.
- Schwarz_triangle wikiPageWikiLink Octahedral_symmetry.
- Schwarz_triangle wikiPageWikiLink PSL(2,7).
- Schwarz_triangle wikiPageWikiLink Regular_Polytopes_(book).
- Schwarz_triangle wikiPageWikiLink Regular_hyperbolic_tiling.
- Schwarz_triangle wikiPageWikiLink Riemann_surface.
- Schwarz_triangle wikiPageWikiLink Simple_group.
- Schwarz_triangle wikiPageWikiLink Special_right_triangles.
- Schwarz_triangle wikiPageWikiLink Sphere.
- Schwarz_triangle wikiPageWikiLink Spherical_triangle.
- Schwarz_triangle wikiPageWikiLink Spherical_trigonometry.
- Schwarz_triangle wikiPageWikiLink Tessellation.
- Schwarz_triangle wikiPageWikiLink Tetrahedral_symmetry.
- Schwarz_triangle wikiPageWikiLink Triangle_group.
- Schwarz_triangle wikiPageWikiLink Uniform_polyhedron.
- Schwarz_triangle wikiPageWikiLink Uniform_star_polyhedron.
- Schwarz_triangle wikiPageWikiLink Uniform_tilings_in_hyperbolic_plane.
- Schwarz_triangle wikiPageWikiLink Vertex_angle.
- Schwarz_triangle wikiPageWikiLink Von_Dyck_group.
- Schwarz_triangle wikiPageWikiLink Wythoff_construction.
- Schwarz_triangle wikiPageWikiLink Wythoff_symbol.
- Schwarz_triangle wikiPageWikiLink File:H2checkers_iii.png.
- Schwarz_triangle wikiPageWikiLink File:Order-3_octakis_octagonal_tiling.png.
- Schwarz_triangle wikiPageWikiLink File:Order-4_bisected_pentagonal_tiling.png.
- Schwarz_triangle wikiPageWikiLink File:Schwarz_triangle_graph.png.
- Schwarz_triangle wikiPageWikiLink File:Schwarz_triangle_on_sphere.png.
- Schwarz_triangle wikiPageWikiLink File:Sphere_symmetry_group_d2h.png.
- Schwarz_triangle wikiPageWikiLink File:Sphere_symmetry_group_d3h.png.
- Schwarz_triangle wikiPageWikiLink File:Sphere_symmetry_group_ih.png.
- Schwarz_triangle wikiPageWikiLink File:Sphere_symmetry_group_oh.png.
- Schwarz_triangle wikiPageWikiLink File:Sphere_symmetry_group_td.png.
- Schwarz_triangle wikiPageWikiLink File:Tile_3,6.svg.
- Schwarz_triangle wikiPageWikiLink File:Tile_V46b.svg.
- Schwarz_triangle wikiPageWikiLink File:Tile_V488_bicolor.svg.
- Schwarz_triangle wikiPageWikiLink File:Uniform_dual_tiling_433-t012.png.
- Schwarz_triangle wikiPageWikiLink File:Uniform_dual_tiling_443-t012.png.
- Schwarz_triangle wikiPageWikiLinkText "Schwarz triangle".
- Schwarz_triangle wikiPageWikiLinkText "Schwarz triangle#Möbius triangles for the sphere".
- Schwarz_triangle wikiPageWikiLinkText "Schwarz_triangle#M.C3.B6bius_triangles".
- Schwarz_triangle wikiPageWikiLinkText "Schwarz_triangle#Mobius_triangles".
- Schwarz_triangle wikiPageWikiLinkText "triangle on the sphere".
- Schwarz_triangle hasPhotoCollection Schwarz_triangle.
- Schwarz_triangle title "Schwarz triangle".
- Schwarz_triangle urlname "SchwarzTriangle".
- Schwarz_triangle wikiPageUsesTemplate Template:CDD.
- Schwarz_triangle wikiPageUsesTemplate Template:Citation.
- Schwarz_triangle wikiPageUsesTemplate Template:Harv.
- Schwarz_triangle wikiPageUsesTemplate Template:KlitzingPolytopes.
- Schwarz_triangle wikiPageUsesTemplate Template:Mathworld.
- Schwarz_triangle wikiPageUsesTemplate Template:Refbegin.
- Schwarz_triangle wikiPageUsesTemplate Template:Refend.
- Schwarz_triangle wikiPageUsesTemplate Template:Reflist.
- Schwarz_triangle wikiPageUsesTemplate Template:Tessellation.
- Schwarz_triangle subject Category:Polyhedra.
- Schwarz_triangle subject Category:Spherical_trigonometry.
- Schwarz_triangle hypernym Triangle.
- Schwarz_triangle type Place.
- Schwarz_triangle type Polytope.
- Schwarz_triangle comment "In geometry, a Schwarz triangle, named after Hermann Schwarz, is a spherical triangle that can be used to tile a sphere, possibly overlapping, through reflections in its edges. They were classified in (Schwarz 1873).These can be defined more generally as tessellations of the sphere, the Euclidean plane, or the hyperbolic plane.".
- Schwarz_triangle label "Schwarz triangle".
- Schwarz_triangle sameAs Triangulo_de_Schwarz.