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- Q3890103 subject Q7035965.
- Q3890103 subject Q7484878.
- Q3890103 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.".
- Q3890103 thumbnail Schwarz_triangle_on_sphere.png?width=300.
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- Q3890103 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.".
- Q3890103 label "Schwarz triangle".
- Q3890103 depiction Schwarz_triangle_on_sphere.png.
