Enneazetton

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Enneazetton
8-simplex t0.svg
Rank8
TypeRegular
SpaceSpherical
Notation
Bowers style acronymEne
Coxeter diagramx3o3o3o3o3o3o3o (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.png)
Schläfli symbol{3,3,3,3,3,3,3}
Tapertopic notation17
Elements
Zetta9 octaexa
Exa36 heptapeta
Peta84 hexatera
Tera126 pentachora
Cells126 tetrahedra
Faces84 triangles
Edges36
Vertices9
Vertex figureOctaexon, edge length 1
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Dizettal angle
Height
Central density1
Number of pieces9
Level of complexity1
Related polytopes
ArmyEne
RegimentEne
DualEnneazetton
ConjugateNone
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryA8, order 362880
ConvexYes
NatureTame

The enneazetton, or ene, also commonly called the 8-simplex, is the simplest possible non-degenerate polyzetton. The full symmetry version has 9 regular octaexa as facets, joining 3 to a hexateron peak and 8 to a vertex, and is one of the 3 regular polyzetta. It is the 8-dimensional simplex.

Vertex coordinates[edit | edit source]

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

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

Representations[edit | edit source]

A regular enneazetton has the following Coxeter diagrams:

  • x3o3o3o3o3o3o3o (full symmetry)
  • ox3oo3oo3oo3oo3oo3oo&#x (A7 axial, octaexal pyramid)

External links[edit | edit source]

  • Klitzing, Richard. "ene".