Rectified 7-simplex

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Rectified 7-simplex
Rank7
TypeUniform
Notation
Bowers style acronymRoc
Coxeter diagramo3x3o3o3o3o3o ()
Elements
Exa8 heptapeta, 8 rectified heptapeta
Peta56 hexatera, 28 rectified hexatera
Tera168 pentachora, 56 rectified pentachora
Cells280 tetrahedra, 70 octahedra
Faces56+280 triangles
Edges168
Vertices28
Vertex figureHexateric prism, edge length 1
Measures (edge length 1)
Circumradius
Hypervolume
Diexal anglesRil–hix–hop:
 Ril–rix–ril:
Height
Central density1
Number of external pieces16
Level of complexity6
Related polytopes
ArmyRoc
RegimentRoc
ConjugateNone
Abstract & topological properties
Flag count241920
Euler characteristic2
OrientableYes
Properties
SymmetryA7, order 40320
ConvexYes
NatureTame

The rectified octaexon, or roc, also called the rectified 7-simplex, is a convex uniform polyexon. It consists of 8 regular heptapeta and 8 rectified heptapeta. Two heptapeta and 6 rectified heptapeta join at each hexateric prismatic vertex. As the name suggests, it is the rectification of the octaexon.

It is also a convex segmentoexon, as heptapeton atop rectified heptapeton.

The hecatonicosihexapentacosiheptacontahexaexon, or 321 polytope, can be obtained as the convex hull of two oppositely oriented rectified octaexa.

Vertex coordinates[edit | edit source]

The vertices of a rectified octaexon of edge length 1 can be given in eight dimensions as all permutations of:

Representations[edit | edit source]

A rectified octaexon has the following Coxeter diagrams:

  • o3x3o3o3o3o3o (full symmetry)
  • xo3ox3oo3oo3oo3oo&#x (A6 axial, heptapeton atop rectified heptapeton)
  • oxo oxo3oox3ooo3ooo3ooo&#xt (A5×A1 axial, vertex-first)
  • xoo3oxo oxo3oox3ooo3ooo&#xt (A4×A2 axial, triangle-first)
  • oxo3xoo3ooo oxo3oox3ooo&#xt (A3×A3 axial, octahedron-first)

External links[edit | edit source]