Pentistericantitruncated 6-cube

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Pentistericantitruncated 6-cube
Rank6
TypeUniform
Notation
Bowers style acronymTocagrax
Coxeter diagramx4x3x3o3x3x ()
Elements
Peta12 stericantitruncated 5-cubes
64 stericantellated 5-simplices
192 prismatorhombated pentachoric prisms
60 great rhombated tesseractic prisms
240 octagonal-truncated tetrahedral duoprisms
160 hexagonal-great rhombicuboctahedral duoprisms
Tera640 triangular duoprisms
1920 triangular-square duoprisms
1920 square-hexagonal duoprisms
960 triangular-octagonal duoprisms
640 hexagonal duoprisms
960 hexagonal-octagonal duoprisms
1920 cuboctahedral prisms
1920 truncated tetrahedral prisms
960 great rhombicuboctahedral prisms
384 small rhombated pentachora
384 prismatorhombated pentachora
120 great rhombated tesseracts
Edges80640
Vertices23040
Vertex figureIrregular square tettene
Measures (edge length 1)
Circumradius
Hypervolume
Central density1
Related polytopes
ArmyTocagrax
RegimentTocagrax
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB6, order 46080
ConvexYes
NatureTame

The pentistericantitruncated 6-cube, also called the pentistericantitruncated dodecapeton, tericelligreatorhombated hexeract, or tocagrax, is a convex uniform 6-polytope. It consists of 12 stericantitruncated 5-cubes, 64 stericantellated 5-simplices, 192 prismatorhombated pentachoric prisms, 60 great rhombated tesseractic prisms, 240 octagonal-truncated tetrahedral duoprisms, and 160 hexagonal-great rhombicuboctahedral duoprisms. 1 stericantitruncated 5-cube, 1 stericantellated 5-simplex, 1 prismatorhombated pentachoric prism, 1 great rhombated tesseractic prism, 1 octagonal-truncated tetrahedral duoprism, and 2 hexagonal-great rhombicuboctahedral duoprisms join at each vertex. As the name suggests, it is the pentistericantitruncation of the 6-cube.

Vertex coordinates[edit | edit source]

The coordinates of a pentistericantitruncated 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]