Stericantellated 5-cube

Stericantellated 5-cube
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Carnit
Coxeter diagram	x4o3x3o3x ()
Elements
Tera	80 triangular-square duoprisms, 80 cuboctahedral prisms, 40 small rhombicuboctahedral prisms, 32 small rhombated pentachora, 10 small rhombated tesseracts
Cells	320+320+320 triangular prisms, 160 octahedra, 240+480 cubes, 160 cuboctahedra, 80 small rhombicuboctahedra
Faces	320+640+640 triangles, 240+960+960+960 squares
Edges	960+960+1920
Vertices	960
Vertex figure	Antiduowedge, edge lengths 1 (one base of disphenoid cell and top square) and √2 (remaining edges)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {17+8{\sqrt {2}}}}{2}}\approx 2.66053$
Hypervolume	${\frac {3240+2262{\sqrt {2}}}{15}}\approx 429.26341$
Diteral angles	Srip-co–cope: $\arccos \left(-{\frac {2{\sqrt {5}}}{5}}\right)\approx 153.43495^{\circ }$
	Cope–trip–tisdip: 150°
	Sircope–cube–tisdip: $\arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$
	Srit–sirco–sircope: 135°
	Sircope–cube–cope: 135°
	Srip–trip–sircope: $\arccos \left(-{\frac {\sqrt {10}}{5}}\right)\approx 129.23152^{\circ }$
	Srit–trip–cope: 120°
	Srit–oct–srip: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
Central density	1
Number of external pieces	242
Level of complexity	56
Related polytopes
Army	Carnit
Regiment	Carnit
Dual	Anticupolanotched enneacosihexecontateron
Conjugate	Quasicellirhombipenteractitriacontaditeron
Abstract & topological properties
Flag count	215040
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B5, order 3840
Convex	Yes
Nature	Tame

The stericantellated 5-cube, also called the cellirhombated penteractitriacontaditeron, cellirhombipenteractitriacontaditeron, or carnit, is a convex uniform 5-polytope. It consists of 80 triangular-square duoprisms, 80 cuboctahedral prisms, 40 small rhombicuboctahedral prisms, 32 small rhombated pentachora, and 10 small rhombated tesseracts. 1 triangular-square duoprism, 1 small rhombated tesseract, 1 small rhombated pentachoron, 2 small rhombicuboctahedral prisms, and 2 cuboctahedral prisms join at each vertex. As the name suggests, it is the stericantellation of the 5-cube or its dual 5-orthoplex.

The stericantellated 5-cube contains the vertices of a prismatorhombated hexadecachoric prism and octagonal-great rhombicuboctahedral duoprism.

Vertex coordinates

The vertices of a stericantellated 5-cube of edge length 1 are given by all permutations of:

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

Representations

A stericantellated 5-cube has the following Coxeter diagrams:

• x4o3x3o3x () (full symmetry)
• xxooxx4ooxxoo3xxooxx3oxxxxo&#xt (B₄ axial, small rhombated tesseract-first)

Gallery

• 

  B₄ or D₅ orthographic projection

• 

  B₃, D₄, or A₂

• 

  B₂

• 

  A₃

Related polytopes

The stericantellated 5-cube is the colonel of a regiment of 27 members.

External links

• Klitzing, Richard. "carnit".
• Wikipedia contributors. "Stericantellated 5-cube".