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Regular polyhedron

A regular polyhedron is a polyhedron with regular and congruent polygons as faces. Its symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different equivalent definitions are used; a common one is that the faces are…

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Overview

The regular polyhedra

Characteristics

Duality of the regular polyhedra

History

Regular polyhedra in nature

Further generalisations

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Map overview Semantic statistics

Regular polyhedron

Nodes145
Edges144
Triples25
Avg. degree1.99
Density0.013793
Components1

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Regular polyhedron

Top relations

related to External links · 5
Regular polyhedron → Eric, MathWorld, Misali, Weisstein, YouTube
is a · 3
Regular polyhedron → polyhedron with regular and congruent polygons as faces, regular map whose vertices and edges correspond to the vertices and edges of the original polyhedron, solid
related to Interior points · 3
Regular polyhedron → However, The, Viviani's
related to Equivalent properties · 2
Regular polyhedron → All, The
related to Concentric spheres · 1
Regular polyhedron → An
related to Further generalisations · 1
Regular polyhedron → The
see also · 1
Regular polyhedron → Quasiregular

Important terminology Word statistics

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Important terminology

regular polyhedra polyhedron faces solids dual platonic vertex five polygons vertices one star convex skew kepler around also dodecahedron century

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Regular polyhedronis apolyhedron with regular and congruent polygons as faces0.90text
Regular polyhedronis asolid0.90text
Regular polyhedronis aregular map whose vertices and edges correspond to the vertices and edges of the original polyhedron0.90text
the pentagraminstance ofThis concept of a regular polyhedron would remain unchallenged for almost 2000 years.Regular star polyhedraRegular star polygons0.80text
the pentagraminstance ofRegular star polyhedraRegular star polygons0.80text
complex spacesinstance ofand other spaces0.80text
discovered over the preceding centuryinstance ofand other spaces0.80text
led to the discovery of more new polyhedra such as complex polyhedra which could only take regular geometric form in those spaces.Regular polyhedra in hyperbolic spaceIn H3 hyperbolic spaceinstance ofand other spaces0.80text
paracompact regular honeycombs have Euclidean tiling facetsinstance ofand other spaces0.80text
vertex figures that act like finite polyhedrainstance ofand other spaces0.80text
Polyhedral combinatoricsinstance ofThe second half of the century saw the development of abstract algebraic ideas0.80text
culminating in the idea of an abstract polytope as a partially ordered setinstance ofThe second half of the century saw the development of abstract algebraic ideas0.80text

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