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24-cell

In four-dimensional geometry, the 24-cell is a convex regular 4-polytope, a four-dimensional analogue of a Platonic solid. It is named for the 24 octahedra that form its boundary.

Root systems, Geometric description & Rotations

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Cells
24 {3,4}
Coxeter diagram
or or
Coxeter group
F4, [3,4,3], order 1152 B4, [4,3,3], order 384 D4, [31,1,1], order 192
Dual
Self-dual
Edges
96
Faces
96 {3}

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Overview

Geometric description

Root systems

Rotations

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Related polytopes

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Map overview Semantic statistics

24-cell

Nodes85
Edges84
Triples91
Avg. degree1.98
Density0.023529
Components1

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24-cell

Top relations

related to Voronoi cells and tessellation · 14
24-cell → As, Cartesian, D4, Each, Eight, Euclidean, F4, Hurwitz, It, The, The Schläfli, The Voronoi, Voronoi, With
related to Cell rings · 10
24-cell → Eight, For, Hopf, North Pole, One, Pick, See, South Pole, The, This
related to Root systems · 10
24-cell → B4, C4, D4, F4, Lie, SO, The, These, This, Weyl
related to Geometric description · 8
24-cell → In, It, Its, Like, Schläfli, Schlӓfli, The, Together
is a · 7
24-cell → 24-point 4-polytope, convex four-dimensional polytope boundary, convex hull of its vertices which can be described as the 24 coordinate permutations of, convex regular 4-polytope, example of a parallelotope, fourth in the sequence of six convex regular 4-polytopes, Weyl group of F4
related to Quaternionic interpretation · 7
24-cell → F4, Hurwitz, The, The D4, This, Viewed, When
related to Reflections · 7
24-cell → Although, Any, Consequently, For, Reflections, The, Tracing
related to Chiral symmetry operations · 6
24-cell → Clifford, Each, For, Hopf, Pictured, The
related to Characteristic orthoscheme · 5
24-cell → Coxeter-Dynkin, Every, If, It, The
related to External links · 2
24-cell → Archived, Wayback MachinePetrie

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Important terminology

rotation vertices regular cells 24 vertex displaystyle great rotations planes plane also right group two 5-cell left isoclinic symmetry convex

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
24-cellCells24 {3,4}1.00infobox
24-cellCoxeter diagramor or1.00infobox
24-cellCoxeter groupF4, [3,4,3], order 1152 B4, [4,3,3], order 384 D4, [31,1,1], order 1921.00infobox
24-cellDualSelf-dual1.00infobox
24-cellEdges961.00infobox
24-cellFaces96 {3}1.00infobox
24-cellPetrie polygondodecagon1.00infobox
24-cellPropertiesconvex, isogonal, isotoxal, isohedral1.00infobox
24-cellSchläfli symbol{3,4,3} r{3,3,4} = { 3 3 , 4 } {\displaystyle \left\{{\begin{array}{l}3\\3,4\end{array}}\right\}} {31,1,1} = { 3 3 3 } {\displaystyle \left\{{\begin{array}{l}3\\3\\3\end{array}}…1.00infobox
24-cellTypeConvex regular 4-polytope1.00infobox
24-cellUniform index221.00infobox
24-cellVertex figureCube1.00infobox
24-cellVertices241.00infobox
24-cellis aconvex regular 4-polytope0.90text
24-cellis aconvex four-dimensional polytope boundary0.90text
24-cellis afourth in the sequence of six convex regular 4-polytopes0.90text
24-cellis a24-point 4-polytope0.90text
24-cellis aconvex hull of its vertices which can be described as the 24 coordinate permutations of0.90text
24-cellis aWeyl group of F40.90text
24-cellis aexample of a parallelotope0.90text

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