Pentiruncicantitruncated 6-cube

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Pentiruncicantitruncated 6-cube
Rank6
TypeUniform
Notation
Bowers style acronymTagpox
Coxeter diagramx4x3x3x3o3x ()
Elements
Peta12 runcicantitruncated 5-cubes
64 stericantitruncated 5-simplices
192 prismatorhombated pentachoric prisms
60 great disprismatotesseractihexadecachoric prisms
240 octagonal-cuboctahedral duoprisms
160 triangular-great rhombicuboctahedral duoprisms
Tera1920 triangular-square duoprisms
1280 triangular-hexagonal duoprisms
1920 triangular-octagonal duoprisms
1920 square-hexagonal duoprisms
1440 square-octagonal duoprisms
1920 cuboctahedral prisms
960 truncated tetrahedral prisms
960 truncated octahedral prisms
240 great rhombicuboctahedral prisms
384 prismatorhombated pentachora
384 great rhombated pentachora
120 great disprismatotesseractihexadecachora
Edges80640
Vertices23040
Vertex figureIrregular square tettene
Measures (edge length 1)
Circumradius
Hypervolume
Central density1
Related polytopes
ArmyTagpox
RegimentTagpox
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB6, order 46080
ConvexYes
NatureTame

The pentiruncicantitruncated 6-cube, also called the pentiruncicantitruncated dodecapeton, terigreatoprismated hexeract, or tagpox, is a convex uniform 6-polytope. It consists of 12 runcicantitruncated 5-cubes, 64 stericantitruncated 5-simplices, 192 prismatorhombated pentachoric prisms, 60 great disprismatotesseractihexadecachoric prisms, 240 octagonal-cuboctahedral duoprisms, and 160 triangular-great rhombicuboctahedral duoprisms. 1 runcicantitruncated 5-cube, 1 stericantitruncated 5-simplex, 1 prismatorhombated pentachoric prism, 2 great disprismatotesseractihexadecachoric prisms, 1 octagonal-cuboctahedral duoprism, and 1 triangular-great rhombicuboctahedral duoprism join at each vertex. As the name suggests, it is the pentiruncicantitruncation of the 6-cube.

Vertex coordinates[edit | edit source]

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

  • .

Gallery[edit | edit source]

External links[edit | edit source]