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Klein quartic

In hyperbolic geometry, the Klein quartic, named after Felix Klein, is a compact Riemann surface of genus 3 with the highest possible order automorphism group for this genus, namely order 168 orientation-preserving automorphisms, and 168 × 2 = 336 automorphisms if orientation may be reversed. As such, the Klein quartic is the Hurwitz surface of lowest…

Art, Tiling & 3-dimensional models

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Klein quartic at a glance

The strongest research directions include Tiling and 3-dimensional models. Use the connected concepts below as starting points, not as a keyword checklist.

Regular mapFundamental domainOrder-3 bisected heptagonal tilingUniversal coverScalene trianglesHelaman FergusonSimons Laufer Mathematical Sciences InstituteBerkeley, California

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Overview

Closed and open forms

As an algebraic curve

Quaternion algebra construction

Tiling

Fundamental domain and pants decomposition

Spectral theory

3-dimensional models

Dessin d'enfants

Related Riemann surfaces

Advanced semantic analysis

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Klein quartic

Top relations

related to Related Riemann surfaces · 9
Klein quartic → Bolza, Bring's, First Hurwitz, Geometrically, Hurwitz, Macbeath, More, Riemann, The Klein
related to Spectral theory · 9
Klein quartic → Because, Bolza, Eigenvalues, It, Klein, Laplace, Little, Riemann, The
related to 3-dimensional models · 7
Klein quartic → However, Klein, Klein's, PSL, SO, The, The Klein
related to Affine quartic · 7
Klein quartic → Considering, H2, Here, Klein, Möbius, SL, The
related to Fundamental domain and pants decomposition · 7
Klein quartic → All, Fuchsian, Gauss-Bonnet, The, The Klein, This, Within
related to Tiling · 6
Klein quartic → Given, Hurwitz, Klein's, The, The Klein, This
related to As an algebraic curve · 5
Klein quartic → Klein, P2, Riemannian, The, The Klein
related to Dessin d'enfants · 5
Klein quartic → Belyi, Klein, Riemann, That, The
related to Quaternion algebra construction · 4
Klein quartic → Fuchsian, Klein, Note, The
is a · 2
Klein quartic → Hurwitz surface of lowest possible genus, modular curve X

Important terminology Word statistics

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Important terminology

quartic klein group surface genus hyperbolic automorphism tiling surfaces projective symmetry plane compact riemann closed 24 regular quotient isomorphic also

Entity relationships Subject–Predicate–Object triples

Extracted RDF-like relationships with confidence and source. The table includes structured facts and lower-confidence contextual relations.
SubjectPredicateObjectConfidenceSrc
Klein quarticis aHurwitz surface of lowest possible genus0.90text
Klein quarticis amodular curve X0.90text
Klein quarticrelated to 3-dimensional modelsThe Klein0.60section
Klein quarticrelated to 3-dimensional modelsPSL0.60section
Klein quarticrelated to 3-dimensional modelsSO0.60section
Klein quarticrelated to 3-dimensional modelsHowever0.60section
Klein quarticrelated to 3-dimensional modelsKlein0.60section
Klein quarticrelated to 3-dimensional modelsKlein's0.60section
Klein quarticrelated to 3-dimensional modelsThe0.60section
Klein quarticrelated to Affine quarticThe0.60section
Klein quarticrelated to Affine quarticConsidering0.60section
Klein quarticrelated to Affine quarticSL0.60section

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    Map overview Semantic statistics

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    Klein quartic

    Nodes99
    Edges98
    Triples61
    Avg. degree1.98
    Density0.020202
    Components1
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