Hendecaxennon

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Hendecaxennon
10-simplex t0.svg
Rank10
TypeRegular
SpaceSpherical
Bowers style acronymUx
Info
Coxeter diagramx3o3o3o3o3o3o3o3o3o
Schläfli symbol{3,3,3,3,3,3,3,3,3}
SymmetryA10, order 39916800
ArmyUx
RegimentUx
Elements
Vertex figureDecayotton, edge length 1
Xenna11 decayotta
Yotta55 enneazetta
Zetta165 octaexa
Exa330 heptapeta
Peta462 hexatera
Tera462 pentachora
Cells330 tetrahedra
Faces165 triangles
Edges55
Vertices11
Measures (edge length 1)
Circumradius55/11 ≈ 0.67420
Inradius55/110 ≈ 0.067420
Hypervolume11/116121600 ≈
2.8562 × 10-8
Dixennal angleacos(1/10) ≈ 84.26083°
Height55/10 ≈ 0.74162
Central density1
Euler characteristic0
Related polytopes
DualHendecaxennon
ConjugateHendecaxennon
Properties
ConvexYes
OrientableYes
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:

  • (±1/2, –3/6, –6/12, –10/20, –15/30, –21/42, –7/28, –1/12, –5/30, –55/110),
  • (0, 3/3, –6/12, –10/20, –15/30, –21/42, –7/28, –1/12, –5/30, –55/110),
  • (0, 0, 6/4, –10/20, –15/30, –21/42, –7/28, –1/12, –5/30, –55/110),
  • (0, 0, 0, 10/5, –15/30, –21/42, –7/28, –1/12, –5/30, –55/110),
  • (0, 0, 0, 0, 15/6, –21/42, –7/28, –1/12, –5/30, –55/110),
  • (0, 0, 0, 0, 0, 21/7, –7/28. –1/12, –5/30, –55/110),
  • (0, 0, 0, 0, 0, 0, 7/4, –1/12, –5/30, –55/110),
  • (0, 0, 0, 0, 0, 0, 0, 2/3, –5/30, –55/110),
  • (0, 0, 0, 0, 0, 0, 0, 0, 35/10, –55/110),
  • (0, 0, 0, 0, 0, 0, 0, 0, 0, 55/11).

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

  • (2/2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0).

External links[edit | edit source]

  • Klitzing, Richard. "Ux".