Stericantellated 6-cube

Stericantellated 6-cube
(OFF file)
Rank	6
Type	Uniform
Notation
Bowers style acronym	Crax
Coxeter diagram	x4o3x3o3x3o ()
Elements
Peta	240 square-octahedral duoprisms, 160 triangular-small rhombicuboctahedral duoprisms, 192 small rhombated pentachoric prisms, 64 small birhombidodecatera, 12 cellirhombipenteractitriacontaditera
Tera	1280 triangular duoprisms, 960+960+1920 triangular-square duoprisms, 960 octahedral prisms, 960 cuboctahedral prisms, 480 small rhombicuboctahedral prisms, 384+384 small rhombated pentachora, 60 small rhombated tesseracts
Cells	1920+3840+3840+3840+3840 triangular prisms, 960+960 octahedra, 2880+5760 cubes, 1920 cuboctahedra, 480 small rhombicuboctahedra
Faces	3840+3840+3840+3840 triangles, 1440+5760+11520+11520 squares
Edges	5760+11520+11520
Vertices	5760
Vertex figure	edge-diminished tetrahedral antifastegium, edge lengths 1 (base squares) and √2 (all remaining edges)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {13+6{\sqrt {2}}}{2}}}\approx 3.27760$
Hypervolume	${\frac {56915+40884{\sqrt {2}}}{45}}\approx 2549.63794$
Dipetal angles	Sibrid–srip–srippip: $\arccos \left(-{\frac {\sqrt {30}}{6}}\right)\approx 155.90516^{\circ }$
	Srippip–ope–squoct: $\arccos \left(-{\frac {2{\sqrt {5}}}{5}}\right)\approx 153.43495^{\circ }$
	Trasirco–tisdip–squoct: 150°
	Srippip–tisdip-trasirco: $\arccos \left(-{\frac {\sqrt {15}}{5}}\right)\approx 140.76848^{\circ }$
	Sibrid–triddip–trasirco: 135°
	Carnit–tisdip–squoct: 120°
	Carnit–cope–srippip: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
Central density	1
Number of external pieces	668
Level of complexity	185
Related polytopes
Army	Crax
Regiment	Crax
Conjugate	Quasicellirhombated hexeract
Abstract & topological properties
Flag count	8524800
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B6, order 46080
Convex	Yes
Nature	Tame

The stericantellated 6-cube, also called the stericantellated dodecapeton, cellirhombated hexeract, or crax, is a convex uniform 6-polytope. It consists of 12 stericantellated 5-cubes, 64 bicantellated 5-simplices, 192 small rhombated pentachoric prisms, 240 square-octahedral duoprisms, and 160 triangular-small rhombicuboctahedral duoprisms. 2 stericantellated 5-cubes, 1 bicantellated 5-simplex, 2 small rhombated pentachoric prisms, 1 square-octahedral duoprism, and 2 triangular-small rhombicuboctahedral duoprisms join at each vertex. As the name suggests, it is the stericantellation of the 6-cube.

The cellirhombated hexeract contains the vertices of an inscribed prismatotruncated penteractic prism, octagonal-great rhombated tesseractic duoprism, and great rhombicuboctahedral duoprism.

Vertex coordinates

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

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

Gallery

• 

  B₅ orthographic projection

• 

  B₄

• 

  B₃

• 

  B₂

• 

  A₅

• 

  A₃

Related polytopes

The regiment of the cellirhombated hexeract contains 75 uniform members.

External links

• Klitzing, Richard. "crax".
• Wikipedia contributors. "Stericantellated 6-cube".