14-simplex

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14-simplex
Rank14
TypeRegular
Notation
Coxeter diagramx3o3o3o3o3o3o3o3o3o3o3o3o3o ()
Schläfli symbol{3,3,3,3,3,3,3,3,3,3,3,3,3}
Elements
Tradaka15 13-simplices
Doka105 12-simplices
Henda455 11-simplices
Daka1365 10-simplices
Xenna3003 9-simplices
Yotta5005 8-simplices
Zetta6435 7-simplices
Exa6435 6-simplices
Peta5005 hexatera
Tera3003 pentachora
Cells1365 tetrahedra
Faces455 triangles
Edges105
Vertices15
Vertex figure13-simplex, edge length 1
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Dihedral angle
Height
Central density1
Number of external pieces15
Level of complexity1
Related polytopes
Army14-simplex
Regiment14-simplex
Dual14-simplex
ConjugateNone
Abstract & topological properties
Flag count1307674368000
Euler characteristic0
OrientableYes
Properties
SymmetryA14, order 1307674368000
Flag orbits1
ConvexYes
NatureTame

The 14-simplex (also called the pentadecatradakon) is the simplest possible non-degenerate 14-polytope. The full symmetry version has 15 regular 13-simplices as facets, joining 3 to a facet and 14 to a vertex, and is regular.

Vertex coordinates[edit | edit source]

The vertices of a regular 14-simplex of edge length 1, centered at the origin, are given by:

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

Much simpler coordinates can be given in 15 dimensions, as all permutations of:

  • .