8-orthoplex

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8-orthoplex
Rank8
TypeRegular
Notation
Bowers style acronymEk
Coxeter diagramo4o3o3o3o3o3o3x ()
Schläfli symbol{3,3,3,3,3,3,4}
Bracket notation<IIIIIIII>
Elements
Zetta256 octaexa
Exa1024 heptapeta
Peta1792 hexatera
Tera1792 pentachora
Cells1120 tetrahedra
Faces448 triangles
Edges112
Vertices16
Vertex figureHecatonicosoctaexon, edge length 1
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Dizettal angle
Height
Central density1
Number of external pieces256
Level of complexity1
Related polytopes
ArmyEk
RegimentEk
DualOcteract
ConjugateNone
Abstract & topological properties
Flag count10321920
Euler characteristic0
OrientableYes
Properties
SymmetryB8, order 10321920
ConvexYes
Net count2642657228
NatureTame

The Diacosipentacontahexazetton, or ek, also called the octacross or 8-orthoplex, is a regular polyzetton. It has 256 regular octaexa as facets, joining 4 to a hexateron peak and 128 to a vertex in a hecatonicosoctaexal arrangement. It is the 8-dimensional orthoplex. It is also a hexadecachoric duotegum and square tetrategum.

Vertex coordinates[edit | edit source]

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

Representations[edit | edit source]

A regular diacosipentacontahexazetton has the following Coxeter diagrams:

  • o4o3o3o3o3o3o3x () (full symmetry)
  • o3o3o3o3o3o3x *b3o () (D8 symmetry)
  • xo3oo3oo3oo3oo3oo3ox&#x (A7 axial, octaexic antiprism)
  • ooo4ooo3ooo3ooo3ooo3ooo3oxo&#xt (B7 axial, hecatonicosoctaexal tegum)

External links[edit | edit source]