Tetradecadokon

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Tetradecadokon
Rank13
TypeRegular
Notation
Coxeter diagramx3o3o3o3o3o3o3o3o3o3o3o3o ()
Schläfli symbol{3,3,3,3,3,3,3,3,3,3,3,3}
Elements
Doka14 tridecahenda
Henda91 dodecadaka
Daka364 hendecaxenna
Xenna1001 decayotta
Yotta2002 enneazetta
Zetta3003 octaexa
Exa3432 heptapeta
Peta3003 hexatera
Tera2002 pentachora
Cells1001 tetrahedra
Faces364 triangles
Edges91
Vertices14
Vertex figureTridecahendon, edge length 1
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Dihedral angle
Height
Central density1
Number of external pieces14
Level of complexity1
Related polytopes
ArmyTetradecadokon
RegimentTetradecadokon
DualTetradecadokon
ConjugateNone
Abstract & topological properties
Flag count87178291200
Euler characteristic2
OrientableYes
Properties
SymmetryA13, order 87178291200
ConvexYes
NatureTame

The tetradecadokon, also commonly called the 13-simplex, is the simplest possible non-degenerate polydokon. The full symmetry version has 14 regular tridecahenda as facets, joining 3 to a dakon and 13 to a vertex, and is one of the 3 regular polydoka. It is the 13-dimensional simplex.

Vertex coordinates[edit | edit source]

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

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

Much simpler coordinates can be given in 14 dimensions, as all permutations of:

  • .