Steriruncicantic 5-cube

Steriruncicantic 5-cube
(OFF file)
Rank	5
Type	Uniform
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	${\frac {86647{\sqrt {2}}}{120}}\approx 1021.14469$
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: $\arccos \left(-{\frac {3}{5}}\right)\approx 126.86990^{\circ }$
	Tah–toe–grip: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
	Tah–tut–grip: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
	Gippid–hip–gippid: $\arccos \left(-{\frac {1}{5}}\right)\approx 101.53696^{\circ }$
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 steriruncicantic 5-cube, also called the great prismatodemipenteract or giphin, is a convex uniform 5-polytope. 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 stericantitruncated 5-orthoplex.

Vertex coordinates

The vertices of a steriruncicantic 5-cube of edge length 1 are given by all permutations and even sign changes of:

• $\left({\frac {7{\sqrt {2}}}{4}},\,{\frac {5{\sqrt {2}}}{4}},\,{\frac {3{\sqrt {2}}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}}\right)$.

Representations

A steriruncicantic 5-cube 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".