Hendecaxennon

From Polytope Wiki
Jump to navigation Jump to search
Hendecaxennon
10-simplex t0.svg
Rank10
TypeRegular
SpaceSpherical
Notation
Bowers style acronymUx
Coxeter diagramx3o3o3o3o3o3o3o3o3o (CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png)
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
DualHendecaxennon
ConjugateNone
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryA10, order 39916800
ConvexYes
NatureTame

The hendecaxennon, or ux, also commonly called the 10-simplex, is the simplest possible non-degenerate polyxennon. The full symmetry version has 11 regular decayotta as facets, joining 3 to an octaexon peak and 10 to a vertex, and is one of the 3 regular polyxenna. 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]

  • Klitzing, Richard. "ux".