Quasiprismatorhombated penteract

Quasiprismatorhombated penteract
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Quiprin
Coxeter diagram	x4/3o3x3x3o ()
Elements
Tera	80 triangular-square duoprisms, 80 truncated tetrahedral prisms, 32 decachora, 10 prismatoquasirhombated tesseracts
Cells	320 triangular prisms, 240 cubes, 320 hexagonal prisms, 160+160 truncated tetrahedra, 40 quasirhombicuboctahedra
Faces	320+320 triangles, 240+480+960 squares, 640 hexagons
Edges	960+960+960
Vertices	960
Vertex figure	Crossed isosceles trapezoidal scalene, base edge lengths 1, √2, √2, √2, opposite edge length 1, lacing lengths √2 and √3
Measures (edge length 1)
Circumradius	${\frac {\sqrt {23-10{\sqrt {2}}}}{2}}\approx 1.48811$
Hypervolume	${\frac {2021-1384{\sqrt {2}}}{6}}\approx 10.62140$
Diteral angles	Paqrit–cube–tisdip: $\arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$
	Paqrit–querco–paqrit: 90°
	Paqrit–tut–deca: $\arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }$
	Paqrit–hip–tuttip: 60°
	Tuttip–trip–tisdip: 30°
	Deca–tut–tuttip: $\arccos \left({\frac {2{\sqrt {5}}}{5}}\right)\approx 26.56505^{\circ }$
Related polytopes
Army	Semi-uniform Pattin'
Regiment	Gibtadin
Conjugate	Prismatorhombated penteract
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	B5, order 3840
Convex	No
Nature	Tame

The quasiprismatorhombated penteract, or quiprin, is a nonconvex uniform polyteron. It consists of 80 triangular-square duoprisms, 80 truncated tetrahedral prisms, 32 decachora, and 10 prismatoquasirhombated tesseracts. 2 prismatoquasirhombated tesseracts, 1 decachoron, 1 triangular-square duoprism, and 2 truncated tetrahedral prisms join at each vertex. It is the quasiruncicantellation of the penteract.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great biprismatotriacontadiadispenteract.

External links

• Bowers, Jonathan. "Category 13: Prismatorhombates and Kin" (#839).

• Klitzing, Richard. "quiprin".