Omnitruncated 6-cube

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Omnitruncated 6-cube
Rank6
TypeUniform
Notation
Bowers style acronymGotaxog
Coxeter diagramx4x3x3x3x3x ()
Elements
Peta12 omnitruncated 5-cubes
64 omnitruncated 5-simplices
192 great prismatodecachoric prisms
60 great disprismatotesseractihexadecachoric prisms
240 octagonal-truncated octahedral duoprisms
160 hexagonal-great rhombicuboctahedral duoprisms
Tera1920+1920 square-hexagonal duoprisms
1440 square-octagonal duoprisms
1280 hexagonal duoprisms
960+960 hexagonal-octahedral duoprisms
960+960+960+960 truncated octahedral prisms
480+480 great rhombicuboctahedral prisms
384+384 great prismatodecachora
120 great disprismatotesseractihexadecachora
Cells5760+5760+5760+5760 cubes
3840+3840+3840+3840+3840 +3840+3840+3840+3840 hexagonal prisms
2880+2880+2880 octagonal prisms
1920+1920+1920 truncated octahedra
960 great rhombicuboctahedra
Faces11520+11520+11520+11520+11520 +11520+11520+11520+11520+11520 squares, 7680+7680+7680+7680 hexagons, 5760 octagons
Edges23040+23040+23040+23040+23040+23040
Vertices46080
Vertex figureIrregular hexateron
Measures (edge length 1)
Circumradius
Hypervolume
Central density1
Related polytopes
ArmyGotaxog
RegimentGotaxog
ConjugateGreat quasiterated hexeractihexacontatetrapeton
Abstract & topological properties
Flag count33177600
Euler characteristic0
OrientableYes
Properties
SymmetryB6, order 46080
ConvexYes
NatureTame

The omnitruncated 6-cube, also called the great terated hexeract, pentisteriruncicantituncated 6-cube, pentisteriruncicantituncated dodecapeton, great terihexeractihexacontatetrapeton, or gotaxog, is a convex uniform 6-polytope. It consists of 12 omnitruncated 5-cubes, 64 omnitruncated 5-simplices, 192 great prismatodecachoric prisms, 60 great disprismatotesseractihexadecachoric prisms, 240 octagonal-truncated octahedral duoprisms, and 160 hexagonal-great rhombicuboctahedral duoprisms. 1 omnitruncated 5-cube, 1 omnitruncated 5-simplex, 1 great prismatodecachoric prism, 1 great disprismatotesseractihexadecachoric prism, 1 octagonal-truncated octahedral duoprism, and 1 hexagonal-great rhombicuboctahedral duoprism join at each vertex. As the name suggests, it is the omnitruncation of the 6-cube.

Coordinates[edit | edit source]

The vertex coordinates of a omnitruncated 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]