Birectified 8-simplex

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Birectified 8-simplex
Rank8
TypeUniform
Notation
Bowers style acronymBrene
Coxeter diagramo3o3x3o3o3o3o3o ()
Elements
Zetta9 rectified octaexa, 9 birectified octaexa
Exa36 heptapeta, 72 rectified heptapeta, 36 birectified heptapeta
Peta252 hexatera, 252 rectified hexatera, 84 dodecatera
Tera756 pentachora, 126+504 rectified pentachora
Cells126+1260 tetrahedra, 630 octahedra
Faces504+1260 triangles
Edges756
Vertices84
Vertex figureTriangular-hexateric duoprism, edge length 1
Measures (edge length 1)
Circumradius1
Hypervolume
Dizettal anglesBroc–ril–roc:
 Broc–bril–broc:
 Roc–hop–roc:
Height
Central density1
Number of external pieces18
Level of complexity21
Related polytopes
ArmyBrene
RegimentBrene
ConjugateNone
Abstract & topological properties
Flag count7620480
Euler characteristic0
OrientableYes
Properties
SymmetryA8, order 362880
ConvexYes
NatureTame

The birectified enneazetton, or brene, also called the birectified 8-simplex, is a convex uniform polyzetton. It consists of 9 rectified octaexa and 9 birectified octaexa. 3 rectified octaexa and 6 birectified octaexa join at each triangular-hexateric duoprismatic vertex. As the name suggests, it is the birectification of the enneazetton.

It is also a convex segmentozetton, as rectified octaexon atop birectified octaexon.

A unit birectified enneazetton can be vetex inscibed into the dischiliahecatonhexaconta-myriaheptachiliadiacosioctaconta-zetton (also konwn as the 421 polytope).

Vertex coordinates[edit | edit source]

The vertices of a birectified enneazetton of edge length 1 can be given in nine dimensions as all permutations of:

Representations[edit | edit source]

A birectified enneazetton has the following Coxeter diagrams:

  • o3o3x3o3o3o3o3o (full symmetry)
  • oo3xo3ox3oo3oo3oo3oo&#x (A7 axial, rectified octaexon atop birectified octaexon)

External links[edit | edit source]