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- 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. In case 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 books?id=Olc5AAAAIAAJ&pg=PA132.
- Schwarz_triangle wikiPageExternalLink purl?GDZPPN002155206.
- Schwarz_triangle wikiPageID "2069325".
- Schwarz_triangle wikiPageRevisionID "605240632".
- Schwarz_triangle hasPhotoCollection Schwarz_triangle.
- Schwarz_triangle title "Schwarz triangle".
- Schwarz_triangle urlname "SchwarzTriangle".
- Schwarz_triangle subject Category:Polyhedra.
- Schwarz_triangle subject Category:Spherical_trigonometry.
- 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 m.06j_m9.
- Schwarz_triangle sameAs Q3890103.
- Schwarz_triangle sameAs Q3890103.
- Schwarz_triangle wasDerivedFrom Schwarz_triangle?oldid=605240632.
- Schwarz_triangle depiction Schwarz_triangle_on_sphere.png.
- Schwarz_triangle isPrimaryTopicOf Schwarz_triangle.
