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Clebsch surface

In mathematics, the Clebsch diagonal cubic surface, or Klein's icosahedral cubic surface, is a non-singular cubic surface, studied by Clebsch (1871) and Klein (1873), all of whose 27 exceptional lines can be defined over the real numbers. The term Klein's icosahedral surface can refer to either this surface or its blowup at the 10 Eckardt points.

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Overview

Definition

  • P4 Projective space

Properties

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Clebsch surface

Nodes15
Edges14
Triples11
Avg. degree1.87
Density0.133333
Components1

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Clebsch surface

Top relations

related to Properties · 5
Clebsch surface → Clebsch, P4, S5, The, Up
is a · 3
Clebsch surface → only cubic surface with this automorphism group.The 27 exceptional lines are, set of points, symmetric group S5 of order 120
related to Definition · 3
Clebsch surface → Eliminating, P4, The Clebsch

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Important terminology

points clebsch surface lines 10 cubic group klein eckardt diagonal 1873 27 klein's icosahedral doi hilbert modular mathematics 1871 exceptional

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Clebsch surfaceis aset of points0.90text
Clebsch surfaceis asymmetric group S5 of order 1200.90text
Clebsch surfaceis aonly cubic surface with this automorphism group.The 27 exceptional lines are0.90text
Clebsch surfacerelated to DefinitionThe Clebsch0.60section
Clebsch surfacerelated to DefinitionP40.60section
Clebsch surfacerelated to DefinitionEliminating0.60section
Clebsch surfacerelated to PropertiesThe0.60section
Clebsch surfacerelated to PropertiesClebsch0.60section
Clebsch surfacerelated to PropertiesS50.60section
Clebsch surfacerelated to PropertiesP40.60section
Clebsch surfacerelated to PropertiesUp0.60section

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    Min side: 3
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