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Schwarz triangle

In geometry, a Schwarz triangle, named after Hermann Schwarz, is a spherical triangle that can be used to tile a sphere (spherical tiling), possibly overlapping, through reflections in its edges. They were classified in Schwarz (1873).

Tessellation by Schwarz triangles, A list of Schwarz triangles & Overview

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Overview

Graphical representation

A list of Schwarz triangles

Tessellation by Schwarz triangles

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Map overview Semantic statistics

Schwarz triangle

Nodes82
Edges81
Triples91
Avg. degree1.98
Density0.02439
Components1

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Schwarz triangle

Top relations

related to Hyperbolic reflection groups · 19
Schwarz triangle → As Joseph Lehner, Automorphic Functions, Carathéodory's, Coxeter, Discontinuous Groups, Dyck, English, Ernest Vinberg, Funktiontheorie, Henri Poincaré, In, Jacques Tits, Let, Lobachevsky, Mathematical Reviews, Schwarz, Siegel's, The, Walther
related to Approach of Siegel · 15
Schwarz triangle → ABC, At, Carl Ludwig Siegel, Elements, If, In, It, Let, Note, Poincaré, Riemann, Schwarz, Siegel's, These, Z2
related to Tessellation by Schwarz triangles · 14
Schwarz triangle → Alternatively, Carathéodory, Evans, Farey, For, Hardy, Hecke, In, Mumford, Riemann, Schottky, Schwarz, Series, Wright
related to Triangles with one or two cusps · 12
Schwarz triangle → By, For, Hecke, In, P1, P2, P3, P4, Pn, Schwarz, The, This
related to Approach of Maskit, de Rham and Beardon · 9
Schwarz triangle → Beardon, Haefliger, Harpe, Maskit, Poincaré's, Rham, Schwarz, Specializing, The Swiss
related to External links · 7
Schwarz triangle → Eric, Klitzing, MathWorld, Richard, Schwarz, The, Weisstein
related to Möbius triangles for the sphere · 6
Schwarz triangle → Dihedral, Icosahedral, Möbius, Octahedral, Schwarz, Tetrahedral
related to Graphical representation · 4
Schwarz triangle → Each, Order-2, Schwarz, The Coxeter-Dynkin
see also · 3
Schwarz triangle → Density, Goursat, Schwarz
is a · 1
Schwarz triangle → smallest hyperbolic Schwarz triangle

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Important terminology

triangle triangles vertex angles plane hyperbolic group two case schwarz angle tessellation one vertices three thus since new tiling half

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Schwarz triangleis asmallest hyperbolic Schwarz triangle0.90text
Schwarz trianglerelated to Approach of Maskit, de Rham and BeardonMaskit0.60section
Schwarz trianglerelated to Approach of Maskit, de Rham and BeardonPoincaré's0.60section
Schwarz trianglerelated to Approach of Maskit, de Rham and BeardonRham0.60section
Schwarz trianglerelated to Approach of Maskit, de Rham and BeardonSpecializing0.60section
Schwarz trianglerelated to Approach of Maskit, de Rham and BeardonSchwarz0.60section
Schwarz trianglerelated to Approach of Maskit, de Rham and BeardonBeardon0.60section
Schwarz trianglerelated to Approach of Maskit, de Rham and BeardonThe Swiss0.60section
Schwarz trianglerelated to Approach of Maskit, de Rham and BeardonHarpe0.60section
Schwarz trianglerelated to Approach of Maskit, de Rham and BeardonHaefliger0.60section
Schwarz trianglerelated to Approach of SiegelIn0.60section
Schwarz trianglerelated to Approach of SiegelCarl Ludwig Siegel0.60section

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    Min side: 3
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