Runcinated 6-orthoplex

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Runcinated 6-orthoplex
Rank6
TypeUniform
Notation
Bowers style acronymSpog
Coxeter diagramo4o3x3o3o3x ()
Elements
Peta160 triangular-octahedral duoprisms
60 icositetrachoric prisms
64 runcinated 5-simplices
12 birectified 5-cubes
Tera1280 triangular duoprisms
384 rectified pentachora
480+960 octahedral prisms
192 small prismatodecachora
120 icositetrachora
Cells240+960 tetrahedra
1920+1920+3840 triangular prisms
480+1920 octahedra
Faces960+3840+3840 triangles, 5760 squares
Edges1440+5760
Vertices960
Vertex figureTriangle atop gyrated triangular-square duoprism, edge lengths 1 (base duoprism and top triangle), 2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dipetal anglesIcope–ope–troct:
 Spix–triddip–troct: 135°
 Nit–ico–icope: 135°
 Spix–ope–icope:
 Spix–spid–spix
 Nit–rap–spix:
Central density1
Number of external pieces296
Level of complexity56
Related polytopes
ArmySpog
RegimentSpog
ConjugateNone
Abstract & topological properties
Flag count2580480
Euler characteristic0
OrientableYes
Properties
SymmetryB6, order 46080
ConvexYes
NatureTame

The runcinated 6-orthoplex, also called the runcinated hexacontatetrapeton, small prismated hexacontatetrapeton, or spog, is a convex uniform 6-polytope. It consists of 12 birectified 5-cubes, 64 runcinated 5-simplices, 60 icositetrachoric prisms, and 160 triangular-octahedral duoprisms. 1 birectified 5-cube, 4 runcinated 5-simplices, 3 icositetrachoric prisms, and 3 triangular-octahedral duoprisms join at each vertex. As the name suggests, it is the runcination of the 6-orthoplex.

The runcinated 6-orthoplex contains the vertices and edges of the square-rectified icositetrachoric duoprism and cuboctahedral-truncated octahedral duoprism.

Vertex coordinates[edit | edit source]

The coordinates of a runcinated 6-orthoplex, centered at the origin and with unit edge length, are given by all permutations of:

  • .

Representations[edit | edit source]

A runcinated 6-orthoplex has the following Coxeter diagrams:

  • o4o3x3o3o3x () (full symmetry)
  • o3x3o3o3x *b3o () (D6 symmetry)

Gallery[edit | edit source]

External links[edit | edit source]