Rectified 8-orthoplex

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Rectified 8-orthoplex
Rank8
TypeUniform
Notation
Bowers style acronymRek
Coxeter diagramo4o3o3o3o3o3x3o ()
Elements
Zetta256 rectified octaexa, 16 hecatonicosoctaexa
Exa2048 heptapeta, 1024 rectified heptapeta
Peta7168 hexatera, 1792 rectified hexatera
Tera10752 pentachora, 1792 rectified pentachora
Cells8960 tetrahedra, 1120 octahedra
Faces448+4480 triangles
Edges1344
Vertices112
Vertex figureHexacontatetrapetic prism, edge length 1
Measures (edge length 1)
Circumradius1
Hypervolume
Dizettal anglesRoc–ril–roc:
 Zee–hop–roc:
Central density1
Number of external pieces272
Level of complexity7
Related polytopes
ArmyRek
RegimentRek
ConjugateNone
Abstract & topological properties
Flag count72253440
Euler characteristic0
OrientableYes
Properties
SymmetryB8, order 10321920
ConvexYes
NatureTame

The rectified diacosipentacontahexazetton, or rek, also called the rectified 8-orthoplex, is a convex uniform polyzetton. It consists of 16 regular hecatonicosoctaexa and 256 rectified octaexa. Two hecatonicosoctaexa and 64 rectified octaexa join at each hexacontatetrapetic prismatic vertex. As the name suggests, it is the rectification of the diacosipentacontahexazetton.

The rectified diacosipentacontahexazetton can be vertex-inscribed into the dischiliahecatonhexaconta-myriaheptachiliadiacosioctaconta-zetton (or 421 polytope).

Vertex coordinates[edit | edit source]

The vertices of a rectified diacosipentacontahexazetton of edge length 1 are given by all permutations of:

Representations[edit | edit source]

A rectified diacosipentacontahexazetton has the following Coxeter diagrams:

  • o4o3o3o3o3o3x3o (full symmetry)
  • o3o3o *b3o3o3o3x3o (D8 symmetry)
  • ooo4ooo3ooo3ooo3ooo3oxo3xox&#xt (B7 axial, hecatonicosoctaexon-first)

External links[edit | edit source]