11-simplex

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11-simplex
Rank11
TypeRegular
Notation
Coxeter diagramx3o3o3o3o3o3o3o3o3o3o ()
Schläfli symbol{3,3,3,3,3,3,3,3,3,3}
Elements
Daka12 10-simplices
Xenna66 9-simplices
Yotta220 8-simplices
Zetta495 7-simplices
Exa792 6-simplices
Peta924 5-simplices
Tera792 pentachora
Cells495 tetrahedra
Faces220 triangles
Edges66
Vertices12
Vertex figure10-simplex, edge length 1
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Dihedral angle
Height
Central density1
Number of external pieces12
Level of complexity1
Related polytopes
Army*
Regiment*
Dual11-simplex
ConjugateNone
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryA11, order 479001600
Flag orbits1
ConvexYes
NatureTame

The 11-simplex, also called the dodecadakon, is the simplest possible non-degenerate 11-polytope. The full symmetry version has 12 regular 10-simplices as facets, joining 3 to a yotton peak and 11 to a vertex, and is one of the 3 regular 11-polytopes. It is the 11-dimensional simplex.

A regular 11-simplex of edge length can be inscribed in the 11-cube. The next largest simplex that can be inscribed in a hypercube is the hexadecatedakon.[1]

Vertex coordinates[edit | edit source]

The vertices of a regular 11-simplex of edge length 1, centered at the origin, are given by:

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

Much simpler coordinates can be given in 12 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.