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5-cell

In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol {3,3,3}. It is a 5-vertex four-dimensional object bounded by five tetrahedral cells. It is also known as a C5, hypertetrahedron, pentachoron, pentatope, pentahedroid, tetrahedral pyramid, or 4-simplex (Coxeter's α4 polytope), the simplest possible convex 4-polytope, and is analogous to…

Properties, Irregular 5-cells & Construction

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Key facts & relationships

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Cells
5 {3,3}
Coxeter group
A4, [3,3,3]
Dual
Self-dual
Edges
10
Faces
10 {3}
Petrie polygon
pentagon

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Overview

Properties

Irregular 5-cells

Construction

Compound

Related polytopes and honeycombs

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Map overview Semantic statistics

5-cell

Nodes78
Edges77
Triples78
Avg. degree1.97
Density0.025641
Components1

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5-cell

Top relations

related to External links · 14
5-cell → AppletsPyrochoron, Der, Eric, German, Jonathan Bowers, Klitzing, Marco Möller's Regular, MathWorld, Pentatope, R4, Regular, Richard, Weisstein, Zeller
related to Orthoschemes · 8
5-cell → An, Each, For, If, In, Orthoschemes, The, Therefore
is a · 5
5-cell → 4-dimensional pyramid with a tetrahedral base and four tetrahedral sides.The regular 5-cell is bounded by five regular tetrahedra, 4-dimensional simplex, convex 4-polytope with Schläfli symbol, polychoron analogous to a tetrahedron in high dimension, solution to the problem
related to As a Boerdijk–Coxeter helix · 5
5-cell → Boerdijk, Clifford, Coxeter, Petrie, The
related to Geodesics and rotations · 5
5-cell → Below, Each, It, The, The Clifford
related to Properties · 5
5-cell → Any, In, It, Its, The
related to As a configuration · 4
5-cell → All, Branko Grünbaum's Venn, The, This
related to Related polytopes and honeycombs · 4
5-cell → Coxeter, Euclidean, It, The
related to Compound · 3
5-cell → A5 Coxeter, The, This
related to Irregular 5-cells · 3
5-cell → Although, In, These

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Important terminology

regular polytopes coxeter tetrahedral edges vertex 10 characteristic vertices tetrahedron four edge three one 4-orthoscheme orthoscheme cells convex uniform polytope

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
5-cellCells5 {3,3}1.00infobox
5-cellCoxeter groupA4, [3,3,3]1.00infobox
5-cellDualSelf-dual1.00infobox
5-cellEdges101.00infobox
5-cellFaces10 {3}1.00infobox
5-cellPetrie polygonpentagon1.00infobox
5-cellPropertiesconvex, isogonal, isotoxal, isohedral, projectively unique1.00infobox
5-cellSchläfli symbol{3,3,3}1.00infobox
5-cellTypeConvex regular 4-polytope1.00infobox
5-cellUniform index11.00infobox
5-cellVertex figure(tetrahedron)1.00infobox
5-cellVertices51.00infobox
5-cellis aconvex 4-polytope with Schläfli symbol0.90text
5-cellis a4-dimensional pyramid with a tetrahedral base and four tetrahedral sides.The regular 5-cell is bounded by five regular tetrahedra0.90text
5-cellis asolution to the problem0.90text
5-cellis a4-dimensional simplex0.90text
5-cellis apolychoron analogous to a tetrahedron in high dimension0.90text

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