Pentisteriruncicantic 6-cube

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Pentisteriruncicantic 6-cube
Rank6
TypeUniform
Notation
Bowers style acronymGochax
Coxeter diagramx3x3x3x3x *b3o ()
Elements
Peta12 steriruncicantic 5-cubes, 32 runcicantitruncated 5-simplices, 32 omnitruncated 5-simplices, 160 hexagonal-truncated tetrahedral duoprisms, 60 tesseractihexadecachoric prisms
Tera640 triangular-hexagonal duoprisms, 640 hexagonal duoprisms, 1440 truncated tetrahedral prisms, 720 truncated octahedral prisms, 192 great rhombated pentachora, 384 great prismatodecachora, 120 tesseractihexadecachora
Edges34560
Vertices11520
Vertex figureIrregular hexateron
Measures (edge length 1)
Circumradius
Hypervolume
Central density1
Number of external pieces296
Related polytopes
ArmyGochax
RegimentGochax
ConjugateNone
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryD6, order 23040
ConvexYes
NatureTame

The pentisteriruncicantic 6-cube, also called the steriruncicantitruncated 6-demicube, great cellidemihexeract, or gochax, is a convex uniform 6-polytope. It consists of 12 steriruncicantic 5-cubes, 32 runcicantitruncated 5-simplices, 32 omnitruncated 5-simplices, 160 hexagonal-truncated tetrahedral duoprisms, and 60 tesseractihexadecachoric prisms. 1 steriruncicantic 5-cube, 1 runcicantitruncated 5-simplex, 2 omnitruncated 5-simplices, 1 hexagonal-truncated tetrahedral duoprism, and 1 tesseractihexadecachoric prism join at each vertex. As the name suggests, it is the steriruncicantitruncation of the 6-demicube.

Vertex coordinates[edit | edit source]

The coordinates of a pentisteriruncicantic 6-cube, centered at the origin and with unit edge length, are given by all permutations and even sign changes of:

  • .

Representations[edit | edit source]

A pentisteriruncicantic 6-cube has the following Coxeter diagrams:

Gallery[edit | edit source]

External links[edit | edit source]