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Triangle group

In mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle. The triangle can be an ordinary Euclidean triangle, a triangle on the sphere, or a hyperbolic triangle. Each triangle group is the symmetry group of a tiling of the Euclidean plane, the sphere, or the hyperbolic plane…

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Overview

Definition

Classification

Von Dyck groups

Overlapping tilings

History

Applications

Advanced semantic analysis

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Map overview Semantic statistics

Triangle group

Nodes73
Edges72
Triples67
Avg. degree1.97
Density0.027397
Components1

How this topic connects Entity context

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Triangle group

Top relations

has application · 15
Triangle group → All, Belyi, H3, Hecke, Hq, Hurwitz, In Grothendieck's, More, Riemann, S2, ST, S², The, Tn, Triangle
related to Classification · 8
Triangle group → Bonnet, Each, Euclidean, Gauss, Given, In, Moreover, The
related to Overlapping tilings · 7
Triangle group → For, Möbius, Schwarz, There, These, This, Triangle
related to Von Dyck groups · 7
Triangle group → Denote, Dyck, Euclidean, For, Such, The, Walther
is a · 6
Triangle group → finite symmetry group of a tiling of a unit sphere by spherical triangles, group that can be realized geometrically by sequences of reflections across the sides of a triangle, infinite symmetry group of a certain tessellation, infinite symmetry group of a tiling of the hyperbolic plane by hyperbolic triangles whose angles add up to a number less than π, reflection group that admits a group presentation Δ, symmetry group of a tiling of the Euclidean plane
related to The spherical case · 6
Triangle group → Euclidean, In, Möbius, Spherical, The, Up
related to External links · 5
Triangle group → Creative Commons Attribution/Share-Alike License, Elizabeth, PlanetMath, This, Triangle
related to Definition · 4
Triangle group → Euclidean, Let, The, Therefore
related to The hyperbolic case · 4
Triangle group → All, For, The, There
related to The Euclidean case · 3
Triangle group → Euclidean, The, Up

Important terminology Word statistics

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Important terminology

triangle group groups hyperbolic tiling euclidean triangles plane spherical sphere angles reflections tilings symmetry two reflection modular projective generated order

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Triangle groupis agroup that can be realized geometrically by sequences of reflections across the sides of a triangle0.90text
Triangle groupis asymmetry group of a tiling of the Euclidean plane0.90text
Triangle groupis areflection group that admits a group presentation Δ0.90text
Triangle groupis ainfinite symmetry group of a certain tessellation0.90text
Triangle groupis afinite symmetry group of a tiling of a unit sphere by spherical triangles0.90text
Triangle groupis ainfinite symmetry group of a tiling of the hyperbolic plane by hyperbolic triangles whose angles add up to a number less than π0.90text
Triangle grouphas applicationTriangle0.60section
Triangle grouphas applicationThe0.60section
Triangle grouphas applicationS²0.60section
Triangle grouphas applicationST0.60section
Triangle grouphas applicationTn0.60section
Triangle grouphas applicationMore0.60section

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