12-simplex

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12-simplex
Rank12
TypeRegular
Notation
Coxeter diagramx3o3o3o3o3o3o3o3o3o3o3o ()
Schläfli symbol{3,3,3,3,3,3,3,3,3,3,3}
Elements
Henda13 11-simplices
Daka78 10-simplices
Xenna286 9-simplices
Yotta715 8-simplices
Zetta1287 7-simplices
Exa1716 6-simplices
Peta1716 5-simplices
Tera1287 5-cells
Cells715 tetrahedra
Faces286 triangles
Edges78
Vertices13
Vertex figure11-simplex, edge length 1
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Dihedral angle
Height
Central density1
Number of external pieces13
Level of complexity1
Related polytopes
Dual12-simplex
ConjugateNone
Convex hull12-simplex
Abstract & topological properties
Flag count6227020800
Euler characteristic0
OrientableYes
Properties
SymmetryA12, order 6227020800
Flag orbits1
ConvexYes
NatureTame

The 12-simplex (also called tridecahendon or tridecahendakon) is the simplest possible non-degenerate 12-polytope. The full symmetry version has 13 regular dodecadaka as facets, joining 3 to a ridge and 12 to a vertex, and is one of the 3 convex regular 12-polytopes. It is the 12-dimensional simplex.

Vertex coordinates[edit | edit source]

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

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

Much simpler coordinates can be given in 13 dimensions, as all permutations of:

  • .