Stericantitruncated 5-cube

Stericantitruncated 5-cube
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Cogrin
Coxeter diagram	x4x3x3o3x ()
Elements
Tera	80 cuboctahedral prisms, 80 triangular-octagonal duoprisms, 40 great rhombicuboctahedral prisms, 32 prismatorhombated pentachora, 10 great rhombated tesseracts
Cells	320+320+320 triangular prisms, 480 cubes, 320 hexagonal prisms, 160 truncated tetrahedra, 240 octagonal prisms, 160 cuboctahedra, 80 great rhombicuboctahedra
Faces	640+640 triangles, 960+960+960+960 squares, 640 hexagons, 240 octagons
Edges	960+960+1920+1920
Vertices	1920
Vertex figure	Skew rectangular pyramidal pyramid, base edge lengths 1 and √2, remaining edge lengths √2 (6), √3 (2), and √2+√2 (1)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {41+16{\sqrt {2}}}}{2}}\approx 3.98834$
Hypervolume	${\frac {41080+29863{\sqrt {2}}}{30}}\approx 2777.08865$
Diteral angles	Prip–co–cope: $\arccos \left(-{\frac {2{\sqrt {5}}}{5}}\right)\approx 153.43495^{\circ }$
	Cope–trip–todip: 150°
	Gircope–op–todip: $\arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$
	Prip–trip–todip: $\arccos \left(-{\frac {\sqrt {15}}{5}}\right)\approx 140.76848^{\circ }$
	Gircope–cube–cope: 135°
	Grit–girco–gircope: 135°
	Prip–hip–gircope: $\arccos \left(-{\frac {\sqrt {10}}{5}}\right)\approx 129.23152^{\circ }$
	Grit–trip–cope: 120°
	Grit–tut–prip: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
Central density	1
Number of external pieces	242
Level of complexity	80
Related polytopes
Army	Cogrin
Regiment	Cogrin
Dual	Great rhombipyramidal pyramidal chilliaenneacosicosateron
Conjugate	Quasicelligreatorhombated penteract
Abstract & topological properties
Flag count	307200
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B5, order 3840
Convex	Yes
Nature	Tame

The stericantitruncated 5-cube, also called the celligreatorhombated penteract or cogrin, is a convex uniform 5-polytope. It consists of 80 cuboctahedral prisms, 80 triangular-octagonal duoprisms, 40 great rhombicuboctahedral prisms, 10 great rhombated tesseracts, and 32 prismatorhombated pentachora. 1 prismatorhombated pentachoron, 1 cuboctahedral prism, 1 great rhombated tesseract, 1 triangular-octagonal duoprism, and 2 great rhombicuboctahedral prisms join at each vertex. As the name suggests, it is the stericantitruncation of the 5-cube.

Vertex coordinates

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

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

Gallery

• 

  B₄ or D₅ orthographic projection

• 

  B₃, D₄, or A₂

• 

  B₂

• 

  A₃

Related polytopes

The stericantitruncated 5-cube is the colonel of a three-member regiment that also includes the small retrocelligreatorhombated penteract and small lepidocelligreatorhombated penteract.

External links

• Bowers, Jonathan. "Category 13: Prismatorhombates and Kin" (#847).

• Klitzing, Richard. "cogrin".
• Wikipedia contributors. "Stericantitruncated 5-cube".