Great prismated hexateron

Great prismated hexateron
(OFF file)
Rank	5
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gippix
Coxeter diagram	x3x3x3x3o ()
Elements
Tera	20 triangular-hexagonal duoprisms, 15 truncated tetrahedral prisms, 6 great rhombated pentachora, 6 great prismatodecachora
Cells	60+60 triangular prisms, 60+60 hexagonal prisms, 30 truncated tetrahedra, 15+30 truncated octahedra
Faces	120 triangles, 90+180+180 squares, 60+60+120 hexagons
Edges	180+180+180+360
Vertices	360
Vertex figure	Sphenoidal pyramid, edge lengths 1 (1), √2(5), and √3 (4)
Measures (edge length 1)
Circumradius	$\frac{2\sqrt{15}}{3} ≈ 2.58199$
Hypervolume	$\frac{24997\sqrt3}{240} ≈ 180.40031$
Diteral angles	Tuttip–trip–thiddip: 135°
	Grip–tut–tuttip: $\arccos\left(-\frac{\sqrt{10}}{5}\right) ≈ 129.23152°$
	Grip–trip–thiddip: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505°$
	Gippid–hip–thiddip: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505°$
	Gippid–hip–tuttip: $\arccos\left(-\frac{\sqrt{10}}{10}\right) ≈ 108.43495°$
	Gippid–toe–grip: $\arccos\left(-\frac15\right) ≈ 101.53696°$
	Gippid–toe–gippid: $\arccos\left(\frac15\right) ≈ 78.46304°$
Central density	1
Number of external pieces	47
Level of complexity	60
Related polytopes
Army	Gippix
Regiment	Gippix
Dual	Sphenoidal-pyramidal triacosihexecontateron
Conjugate	None
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	A5, order 720
Convex	Yes
Nature	Tame

The great prismated hexateron, or gippix, also called the runcicantitruncated 5-simplex, is a convex uniform polyteron. It consists of 20 triangular-hexagonal duoprisms, 15 truncated tetrahedral prisms, 6 small rhombated pentachora, and 6 great prismatodecachora. 2 great prismatodecachora, 1 great rhombated pentachoron, 1 truncated tetrahedral prism, and 1 triangular-hexagonal duoprism join at each vertex. As the name suggests, it is the runcicantitruncation of the hexateron.

Vertex coordinates

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

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

Gallery

• 

  A₄ orthographic projection

• 

  A₃

• 

  A₂

External links

• Bowers, Jonathan. "Category 10: Greater Truncates" (#733).

• Klitzing, Richard. "gippix".

• Wikipedia Contributors. "Runcicantitruncated 5-simplex".