10-simplex

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10-simplex
Rank10
TypeRegular
Notation
Bowers style acronymUx
Coxeter diagramx3o3o3o3o3o3o3o3o3o ()
Schläfli symbol{3,3,3,3,3,3,3,3,3}
Tapertopic notation19
Elements
Xenna11 decayotta
Yotta55 enneazetta
Zetta165 octaexa
Exa330 heptapeta
Peta462 hexatera
Tera462 pentachora
Cells330 tetrahedra
Faces165 triangles
Edges55
Vertices11
Vertex figureDecayotton, edge length 1
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Dixennal angle
Height
Central density1
Number of external pieces11
Level of complexity1
Related polytopes
ArmyUx
RegimentUx
Dual10-simplex
ConjugateNone
Abstract & topological properties
Flag count39916800
Euler characteristic0
OrientableYes
SkeletonK11
Properties
SymmetryA10, order 39916800
Flag orbits1
ConvexYes
NatureTame

The 10-simplex, also called the hendecaxennon, is the simplest possible non-degenerate 10-polytope. The full symmetry version has 11 regular 9-simplices as facets, joining 3 to an 7-simplex peak and 10 to a vertex, and is one of the 3 regular 1-polytopes. It is the 10-dimensional simplex.

Vertex coordinates[edit | edit source]

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

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

Much simpler coordinates can be given in 11 dimensions, as all permutations of:

  • .

External links[edit | edit source]