Celligreatorhombated hexateron

Celligreatorhombated hexateron
(OFF file)
Rank	5
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Cograx
Coxeter diagram	x3x3x3o3x ()
Elements
Tera	20 triangular-hexagonal duoprisms, 15 cuboctahedral prisms, 15 truncated octahedral prisms, 6 great rhombated pentachora, 6 prismatorhombated pentachora
Cells	60+60+60 triangular prisms, 90 cubes, 60+60 hexagonal prisms, 30 truncated tetrahedra, 30 cuboctahedra, 30 truncated octahedron
Faces	120+120 triangles, 180+180+180+180 squares, 60+120 hexagons
Edges	180+180+360+360
Vertices	360
Vertex figure	Skew rectangular pyramidal pyramid, base edge lengths 1 and √2, remaining edge lengths √2 (6) and √3 (3)
Measures (edge length 1)
Circumradius	$\frac{\sqrt{195}}{6} ≈ 2.32737$
Hypervolume	$\frac{20297\sqrt3}{240} ≈ 146.48098$
Diteral angles	Tope–hip–thiddip: 135°
	Cope–trip–thiddip: 135°
	Prip–co–cope: $\arccos\left(-\frac{\sqrt{10}}{5}\right) ≈ 129.23152°$
	Grip–toe–tope: $\arccos\left(-\frac{\sqrt{10}}{5}\right) ≈ 129.23152°$
	Cope–cube–tope: 120°
	Prip–hip–thiddip: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505°$
	Grip–trip–thiddip: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505°$
	Prip–trip–cope: $\arccos\left(-\frac{\sqrt{10}}{10}\right) ≈ 108.43495°$
	Prip–tut–grip: $\arccos\left(-\frac15\right) ≈ 101.53696°$
Central density	1
Number of external pieces	62
Level of complexity	80
Related polytopes
Army	Cograx
Regiment	Cograx
Dual	Deltopyramidal pyramidal triacosihexecontateron
Conjugate	None
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	A5, order 720
Convex	Yes
Nature	Tame

The celligreatorhombated hexateron, or cograx, also called the stericantitruncated 5-simplex, is a convex uniform polyteron. It consists of 20 triangular-hexagonal duoprisms, 15 cuboctahedral prisms, 15 truncated octahedral prisms, 6 great rhombated pentachora, and 6 prismatorhombated pentachora. 1 prismatorhombated pentachoron, 1 cuboctahedral prism, 1 great rhombated pentachoron, 1 triangular-hexagonal duoprism, and 2 truncated octahedral prisms join at each vertex. As the name suggests, it is the stericantitruncation of the hexateron.

Vertex coordinates

The vertices of a celligreatorhombated hexateron of edge length 1 can be given in 6 dimensions as all permutations of:

• $\left(2\sqrt2,\,\frac{3\sqrt2}{2},\,\sqrt2,\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,0\right).$

Gallery

• 

  A₄ orthographic projection

• 

  A₃

• 

  A₂

Related polytopes

The celligreatorhombated hexateron is the colonel of a three-member regiment that also includes the retrocelligreatorhombated hexateron and lepidocelligreatorhombated hexateron.

External links

• Bowers, Jonathan. "Category 13: Prismatorhombates and Kin" (#841).

• Klitzing, Richard. "cograx".

• Wikipedia Contributors. "Stericantitruncated 5-simplex".