Runcicantitruncated 6-cube

Runcicantitruncated 6-cube
Rank	6
Type	Uniform
Notation
Bowers style acronym	Gippox
Coxeter diagram	x4x3x3x3o3o ()
Elements
Peta	12 runcicantitruncated 5-cubes 64 cantitruncated 5-simplices 192 truncated pentachoric prisms 240 octagonal-tetrahedral duoprisms
Tera	960 truncated tetrahedral prisms 1920 tetrahedral prisms 960 triangular-octahedral duoprisms 384 truncated pentachora 384 small rhombated pentachora 384 great rhombated pentachora 60 great disprismatotesseractihexadecachora
Edges	23040
Vertices	7680
Vertex figure	Irregular hexateron
Measures (edge length 1)
Circumradius	${\sqrt {\frac {35+12{\sqrt {2}}}{2}}}\approx 5.09758$
Hypervolume	${\frac {314671+206322{\sqrt {2}}}{30}}\approx 20215.14569$
Central density	1
Related polytopes
Army	Gippox
Regiment	Gippox
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B6, order 46080
Convex	Yes
Nature	Tame

The runcicantitruncated 6-cube, also called the runcicantitruncated dodecapeton, great prismated hexeract, or gippox, is a convex uniform 6-polytope. It consists of 12 runcicantitruncated 5-cubes, 64 cantitruncated 5-simplices, 192 truncated pentachoric prisms, and 240 octagonal-tetrahedral duoprisms. 3 runcicantitruncated 5-cubes, 1 cantitruncated 5-simplex, 1 truncated pentachoric prism, and 1 octagonal-tetrahedral duoprism join at each vertex. As the name suggests, it is the runcicantitruncation of the 6-cube.

Vertex coordinates

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

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

Gallery

• 

  B₅ orthographic projection

• 

  B₄

• 

  B₃

• 

  B₂

• 

  A₅

• 

  A₃

External links

• Wikipedia contributors. "Runcicantitruncated 6-cube".