Great prismatodemipenteract

Great prismatodemipenteract
(OFF file)
Rank	5
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Giphin
Coxeter diagram	x3x3x3x *b3o ()
Elements
Tera	40 truncated tetrahedral prisms, 16 great rhombated pentachora, 10 tesseractihexadecachora, 16 great prismatodecachora
Cells	160 triangular prisms, 80+160 hexagonal prisms, 80+80 truncated tetrahedra, 80+80 truncated octahedra
Faces	320 triangles, 240+240+480 squares, 160+320+320 hexagons
Edges	480+480+480+960
Vertices	960
Vertex figure	Sphenoidal pyramid, edge lengths 1 (1), √2(4), and √3 (5)
Measures (edge length 1)
Circumradius	$\frac{\sqrt{170}}{4} \approx 3.25960$
Hypervolume	$\frac{86647\sqrt2}{120} \approx 1021.14469$
Diteral angles	Grip–trip–tuttip: $\arccos\left(-\frac{\sqrt{15}}{5}\right) \approx 140.76848^\circ$
	Tah–tut–tuttip: 135°
	Gippid–hip–tuttip: $\arccos\left(-\frac{\sqrt{10}}{5}\right) \approx 129.23152^\circ$
	Grip–toe–gippid: $\arccos\left(-\frac35\right) \approx 126.86990^\circ$
	Tah–toe–grip: $\arccos\left(-\frac{\sqrt5}{5}\right) \approx 116.56505^\circ$
	Tah–tut–grip: $\arccos\left(-\frac{\sqrt5}{5}\right) \approx 116.56505^\circ$
	Gippid–hip–gippid: $\arccos\left(-\frac15\right) \approx 101.53696^\circ$
Central density	1
Number of external pieces	82
Level of complexity	60
Related polytopes
Army	Giphin
Regiment	Giphin
Dual	Sphenoidal-pyramidal enneacosihexecontateron
Conjugate	None
Abstract & topological properties
Flag count	115200
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	D5, order 1920
Convex	Yes
Nature	Tame

The great prismatodemipenteract, or giphin, also called the steriruncicantic 5-cube, is a convex uniform polyteron. It consists of 40 truncated tetrahedral prisms, 16 great rhombated pentachora, 10 tesseractihexadecachora, and 16 great prismatodecachora. 2 great prismatodecachora, 1 great rhombated pentachoron, 1 tesseractihexadecachoron, and 1 trunctaed tetrahedral prism join at each vertex. It can be formed from an alternated faceting of the celligreatorhombated triacontaditeron.

Vertex coordinates

The vertices of a great prismatodemipenteract of edge length 1 are given by all permutations and even sign changes of:

• $\left(\frac{7\sqrt2}{4},\,\frac{5\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right)$.

Representations

A great prismatodemipenteract has the following Coxeter diagrams:

• x3x3x3x *b3o () (full symmetry)
• s4o3x3x3x () (as alternated faceting)

Gallery

• 

  B₅ orthographic projection

• 

  D₄

• 

  D₃

• 

  A₃

External links

• Bowers, Jonathan. "Category 10: Greater Truncates" (#741).

• Klitzing, Richard. "giphin".

• Wikipedia Contributors. "Steriruncicantic 5-cube".