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16-cell

In geometry, the 16-cell is the regular convex 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,4}. It is one of the six regular convex 4-polytopes first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century. It is also called C16, hexadecachoron, or hexdecahedroid .

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Cells
16 {3,3}
Coxeter group
B4, [3,3,4], order 384 D4, order 192
Dual
Tesseract
Edges
24
Faces
32 {3}
Petrie polygon
octagon

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Overview

Geometry

Tessellations

Projections

4 sphere Venn diagram

Symmetry constructions

Related complex polygons

Related uniform polytopes and honeycombs

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Map overview Semantic statistics

16-cell

Nodes98
Edges97
Triples75
Avg. degree1.98
Density0.020408
Components1

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16-cell

Top relations

related to External links · 13
16-cell → Archived, Cell, Der, Description, Eric, German, Marco Möller's Regular, MathWorld, R4, Richard, Wayback MachineKlitzing, Weisstein, Zeller
related to Tessellations · 10
16-cell → Each, Euclidean, Hence, One, R4, Schläfli, The, This, Together, Twenty-four
related to Structure · 6
16-cell → At, It, Its, The, The Schläfli, There
is a · 5
16-cell → 4-dimensional cross polytope, regular convex 4-polytope, second in the sequence of 6 convex regular 4-polytopes, simple frame in which to observe 4-dimensional rotations, simplest regular polytope in which they occur
related to Related complex polygons · 5
16-cell → It, Its, Kantor, The, The Möbius
related to Rotations · 5
16-cell → Completely, Euclidean, In, Rotations, The
related to Symmetry constructions · 5
16-cell → B4, Coxeter, It, The, There
related to Coordinates · 3
16-cell → All, Cartesian, The
related to Projections · 3
16-cell → In, Surrounding, The
related to Related uniform polytopes and honeycombs · 3
16-cell → B4, D4, The

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Important terminology

vertices regular edges orthogonal vertex three cells tetrahedral one two squares symmetry octahedron planes tetrahedra completely tetrahedron also great rotation

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
16-cellCells16 {3,3}1.00infobox
16-cellCoxeter groupB4, [3,3,4], order 384 D4, order 1921.00infobox
16-cellDualTesseract1.00infobox
16-cellEdges241.00infobox
16-cellFaces32 {3}1.00infobox
16-cellPetrie polygonoctagon1.00infobox
16-cellPropertiesconvex, isogonal, isotoxal, isohedral, regular, Hanner polytope1.00infobox
16-cellSchläfli symbol{3,3,4}1.00infobox
16-cellTypeConvex regular 4-polytope 4-orthoplex 4-demicube1.00infobox
16-cellUniform index121.00infobox
16-cellVertex figureOctahedron1.00infobox
16-cellVertices81.00infobox
16-cellis aregular convex 4-polytope0.90text
16-cellis asecond in the sequence of 6 convex regular 4-polytopes0.90text
16-cellis asimple frame in which to observe 4-dimensional rotations0.90text
16-cellis asimplest regular polytope in which they occur0.90text
16-cellis a4-dimensional cross polytope0.90text

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