Icosiheptaheptacontadipetic prism

Icosiheptaheptacontadipetic prism
File:Icosiheptaheptacontadipetic prism.png
Rank	7
Type	Uniform
Notation
Bowers style acronym	Jakip
Coxeter diagram	x x3o3o3o3o *d3o ()
Elements
Exa	72 hexateric prisms, 27 triacontaditeric prisms, 2 icosiheptaheptacontadipeta
Peta	144 hexatera, 216+432 pentachoric prisms, 54 hexadecachoric prisms
Tera	432+864 pentachora, 1080 tetrahedral prisms
Cells	2160 tetrahedra 720 triangular prisms
Faces	1440 triangles, 216 squares
Edges	27+432
Vertices	54
Vertex figure	Demipenteractic pyramid, edge lengths 1 (base), √2 (legs)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {33}}{6}}\approx 0.95743$
Hypervolume	${\frac {\sqrt {3}}{16}}\approx 0.10825$
Diexal angles	Taccup–penp–hixip: $\arccos \left(-{\frac {\sqrt {6}}{4}}\right)\approx 127.76124^{\circ }$
	Taccup–penp–taccup: $\arccos \left(-{\frac {1}{4}}\right)\approx 104.47751^{\circ }$
	Jak–tac–taccup: 90°
	Jak–hix–hixip: 90°
Height	1
Central density	1
Number of external pieces	101
Level of complexity	21
Related polytopes
Army	Jakip
Regiment	Jakip
Dual	Semistellatotriacontaditeric icosiheptapeton tegum
Conjugate	None
Abstract & topological properties
Flag count	2177280
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	E6×A1, order 103680
Convex	Yes
Nature	Tame

The icosiheptaheptacontadipetic prism or jakip is a prismatic uniform polyexon that consists of 2 icosiheptaheptacontadipeta, 27 triacontaditeric prisms, and 72 hexateric prisms as facets. Each vertex joins 1 icosiheptaheptacontadipeton, 10 triacontaditeric prisms, and 16 hexateric prisms. As the name suggests, it is a prism based on the icosiheptaheptacontadipeton, which also makes it a convex segmentoexon.

Vertex coordinates

The vertices of an icosiheptaheptacontadipetic prism of edge length 1, centered at the origin, are given by:

• $\left(0,\,0,\,0,\,0,\,0,\,{\frac {\sqrt {6}}{3}},\,\pm {\frac {1}{2}}\right),$
• $\left({\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {6}}{12}},\,\pm {\frac {1}{2}}\right)$ and all even sign changes of the first five coordinates,
• $\left(\pm {\frac {\sqrt {2}}{2}},\,0,\,0,\,0,\,0,\,-{\frac {\sqrt {6}}{6}},\,\pm {\frac {1}{2}}\right)$ and all permutations of first 5 coordinates.

External links

• Klitzing, Richard. "jakip".