Steriruncicantitruncated 6-cube

Steriruncicantitruncated 6-cube
Rank	6
Type	Uniform
Notation
Bowers style acronym	Gocax
Coxeter diagram	x4x3x3x3x3o ()
Elements
Peta	12 omnitruncated 5-cubes 64 runcicantitruncated 5-simplices 192 great rhombated pentachoric prisms 240 octagonal-truncated tetrahedral duoprisms and 160 triangular-great rhombicuboctahedral duoprisms
Tera	1920 triangular-square duoprisms 1280 triangular-hexagonal duoprisms 960 triangular-octagonal duoprisms 960 hexagonal-octagonal duoprisms 1920 truncated tetrahedral prisms 960 truncated octahedral prisms 240 great rhombicuboctahedral prisms 384 great rhombated pentachora 384 great prismatodecachora 60 great disprismatotesseractihexadecachora
Edges	69120
Vertices	23040
Vertex figure	Irregular hexateron
Measures (edge length 1)
Circumradius	${\sqrt {\frac {49+14{\sqrt {2}}}{2}}}\approx 5.86511$
Hypervolume	${\frac {3615691+2279172{\sqrt {2}}}{90}}\approx 75988.07726$
Central density	1
Related polytopes
Army	Gocax
Regiment	Gocax
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B6, order 46080
Convex	Yes
Nature	Tame

The steriruncicantitruncated 6-cube, also called the steriruncicantitruncated dodecapeton, great cellated hexeract, or gocax, is a convex uniform 6-polytope. It consists of 12 omnitruncated 5-cubes, 64 runcicantitruncated 5-simplices, 192 great rhombated pentachoric prisms, 240 octagonal-truncated tetrahedral duoprisms, and 160 triangular-great rhombicuboctahedral duoprisms. 2 omnitruncated 5-cubes, 1 runcicantitruncated 5-simplex, 1 great rhombated pentachoric prism, 1 octagonal-truncated tetrahedral duoprism, and 1 triangular-great rhombicuboctahedral duoprism join at each vertex. As the name suggests, it is the steriruncicantitruncation of the 6-cube.

Vertex coordinates

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

• $\left(\pm {\frac {1+4{\sqrt {2}}}{2}},\,\pm {\frac {1+4{\sqrt {2}}}{2}},\,\pm {\frac {3+{\sqrt {2}}}{2}},\,\pm {\frac {1+2{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}}\right)$.

Gallery

• 

  B₅ orthographic projection

• 

  B₄

• 

  B₃

• 

  B₂

• 

  A₅

• 

  A₃

External links

• Wikipedia contributors. "Steriruncicantitruncated 6-cube".