Quasiprismated penteract

Quasiprismated penteract
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Quappin
Coxeter diagram	x4/3o3o3x3o ()
Elements
Tera	80 triangular-square duoprisms, 80 octahedral prisms, 32 rectified pentachora, 10 quasidisprismatotesseractihexadecachora
Cells	160 tetrahedra, 320+320 triangular prisms, 160 octahedra, 40+240 cubes
Faces	320+640 triangles, 240+960 squares
Edges	480+960
Vertices	320
Vertex figure	Triangular crossed antifastegium, edge lengths 1 (base triangular prism) and √2 (sides and top triangle)
Measures (edge length 1)
Circumradius	${\frac {2{\sqrt {2}}-1}{2}}\approx 0.91421$
Hypervolume	${\frac {677{\sqrt {2}}-930}{30}}\approx 0.91409$
Diteral angles	Quidpith–cube–quidpith: 90°
	Quidpith–tet–rap: $\arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }$
	Quidpith–trip–ope: 60°
	Quidpith–cube–tisdip: $\arccos \left({\frac {\sqrt {6}}{3}}\right)\approx 35.26439^{\circ }$
	Ope–trip–tisdip: 30°
	Rap–oct–ope: $\arccos \left({\frac {2{\sqrt {5}}}{5}}\right)\approx 26.56505^{\circ }$
Related polytopes
Army	Sirn
Regiment	Fawdint
Conjugate	Small prismated penteract
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	B5, order 3840
Convex	No
Nature	Tame

The quasiprismated penteract, or quappin, is a nonconvex uniform polyteron. It consists of 80 triangular-square duoprisms, 80 octahedral prisms, 32 rectified pentachora, and 10 quasidisprismatotesseractihexadecachoron. One rectified pentachoron, 2 quasidisprismatotesseractihexadecachora, 3 octahedral prisms, and 3 triangular-square duoprisms join at each vertex. It is the quasiruncination of the penteract.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the frustosphenary dispenteractitriacontaditeron.