15-simplex

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15-simplex
Rank15
TypeRegular
Notation
Coxeter diagramx3o3o3o3o3o3o3o3o3o3o3o3o3o3o ()
Schläfli symbol{3,3,3,3,3,3,3,3,3,3,3,3,3,3}
Elements
Tedaka16 14-simplices
Tradaka120 13-simplices
Doka560 12-simplices
Henda1820 11-simplices
Daka4368 10-simplices
Xenna8008 9-simplices
Yotta11440 8-simplices
Zetta12870 7-simplices
Exa11440 6-simplices
Peta8008 hexatera
Tera4368 pentachora
Cells1820 tetrahedra
Faces560 triangles
Edges120
Vertices16
Vertex figure14-simplex, edge length 1
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Dihedral angle
Height
Central density1
Number of external pieces16
Level of complexity1
Related polytopes
Army15-simplex
Regiment15-simplex
Dual15-simplex
ConjugateNone
Abstract & topological properties
Flag count20922789888000
Euler characteristic2
OrientableYes
Properties
SymmetryA15, order 20922789888000
ConvexYes
NatureTame

The 15-simplex (also called the hexadecatedakon) is the simplest possible non-degenerate 15-polytope. The full symmetry version has 16 regular 14-simplices as facets, joining 3 to a facet and 15 to a vertex, and is regular.

A regular hexadecatedakon of edge length 22 can be inscribed in the unit 15-cube.[1]

Vertex coordinates[edit | edit source]

The vertices of a regular 15-simplex of edge length 1, centered at the origin, are given by:

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Simpler sets of coordinates can be found by inscribing the 15-simplex into the 15-cube. One such set is given by:

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Much simpler coordinates can be given in 16 dimensions, as all permutations of:

  • .

References[edit | edit source]

  1. Sloane, N. J. A. (ed.). "Sequence A019442". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.