16-simplex

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16-simplex
Rank16
TypeRegular
Notation
Coxeter diagramx3o3o3o3o3o3o3o3o3o3o3o3o3o3o3o ()
Schläfli symbol{3,3,3,3,3,3,3,3,3,3,3,3,3,3,3}
Elements
Pedaka17 15-simplices
Tedaka136 14-simplices
Tradaka680 13-simplices
Doka2380 12-simplices
Henda6188 11-simplices
Daka12376 10-simplices
Xenna19448 9-simplices
Yotta24310 8-simplices
Zetta24310 7-simplices
Exa19448 6-simplices
Peta12376 hexatera
Tera6188 pentachora
Cells2380 tetrahedra
Faces680 triangles
Edges136
Vertices17
Vertex figure15-simplex, edge length 1
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Dihedral angle
Height
Central density1
Number of external pieces17
Level of complexity1
Related polytopes
Army*
Regiment*
Dual16-simplex
ConjugateNone
Abstract & topological properties
Flag count355687428096000
Euler characteristic0
OrientableYes
Properties
SymmetryA16, order 355687428096000
ConvexYes
NatureTame

The 16-simplex (also called the heptadecapedakon) is the simplest possible non-degenerate 16-polytope. The full symmetry version has 17 regular 15-simplices as facets, joining 3 to a peak and 16 to a vertex, and is regular.

Vertex coordinates[edit | edit source]

The vertices of a regular 16-simplex of edge length 1, centered at the origin, are given by:

  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • .
  • ,
  • .

Much simpler coordinates can be given in 17 dimensions, as all permutations of:

  • .