Runcicantitruncated 5-cube

Runcicantitruncated 5-cube
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Gippin
Coxeter diagram	x4x3x3x3o ()
Elements
Tera	80 truncated tetrahedral prisms, 80 triangular-octagonal duoprisms, 32 great rhombated pentachora, 10 great disprismatotesseractihexadecachora
Cells	320+320 triangular prisms, 160 truncated tetrahedra, 320 hexagonal prisms, 240 octagonal prisms, 160 truncated octahedra, 40 great rhombicuboctahedra
Faces	640 triangles, 480+960+960 squares, 320+640 hexagons, 240 octagons
Edges	960+960+960+1920
Vertices	1920
Vertex figure	Sphenoidal pyramid, edge lengths 1 (1), √2 (5), √3 (3), and √2+√2 (1)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {51+18{\sqrt {2}}}}{2}}\approx 4.37195$
Hypervolume	${\frac {51705+39089{\sqrt {2}}}{30}}\approx 3566.17313$
Diteral angles	Grip–tut–tuttip: $\arccos \left(-{\frac {2{\sqrt {5}}}{5}}\right)\approx 153.43495^{\circ }$
	Tuttip–trip–todip: 150°
	Gidpith–op–todip: $\arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$
	Grip–trip–todip: $\arccos \left(-{\frac {\sqrt {15}}{5}}\right)\approx 140.76848^{\circ }$
	Gidpith–hip–tuttip: 120°
	Gidpith–toe–grip: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
	Gidpith–girco–gidpith: 90°
Central density	1
Number of external pieces	202
Level of complexity	60
Related polytopes
Army	Gippin
Regiment	Gippin
Dual	Great sphenoidal-pyramidal chilliaenneacosicosateron
Conjugate	Great quasiprismated penteract
Abstract & topological properties
Flag count	230400
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B5, order 3840
Convex	Yes
Nature	Tame

The runcicantitruncated 5-cube, also called the great prismated penteract or gippin, is a convex uniform 5-polytope. It consists of 80 truncated tetrahedral prisms, 80 triangular-octagonal duoprisms, 32 great rhombated pentachora, and 10 great disprismatotesseractihexadecachora. 2 great disprismatotesseractihexadecachora, 1 great rhombated pentachoron, 1 truncated tetrahedral prism, and 1 triangular-octagonal duoprism join at each vertex. As the name suggests, it is the runcicantitruncation of the 5-cube.

Vertex coordinates

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

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

Gallery

• 

  B₄ or D₅ orthographic projection

• 

  B₃, D₄, or A₂

• 

  B₂

• 

  A₃

External links

• Bowers, Jonathan. "Category 10: Greater Truncates" (#734).

• Klitzing, Richard. "gippin".
• Wikipedia contributors. "Runcicantitruncated 5-cube".