Pentagrammal antiprismatoverted hexacosihecatonicosachoron

Pentagrammal antiprismatoverted hexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Papvixhi
Coxeter diagram	(o3x3x3o5/2*a)/2 (/2)
Elements
Cells	600 truncated tetrahedra 120 great icosahedra
Faces	2400 triangles 1200 hexagons
Edges	3600
Vertices	720
Vertex figure	Pentagrammic antiprism, edge lengths 1 (base) and √3 (side)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {5+{\sqrt {5}}}{2}}}\approx 1.90211$
Hypervolume	$25{\frac {51+22{\sqrt {5}}}{4}}\approx 626.20935$
Dichoral angles	Tut–6–tut: $\arccos \left(-{\frac {1+3{\sqrt {5}}}{8}}\right)\approx 164.47751^{\circ }$
	Gike–3–tut: $\arccos \left(-{\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 157.76124^{\circ }$
Central density	17
Number of external pieces	32520
Level of complexity	86
Related polytopes
Army	Rox, edge length ${\frac {{\sqrt {5}}-1}{2}}$
Regiment	Righi
Conjugate	Pentagonal retroprismatoverted hexacosihecatonicosachoron
Convex core	Hexacosichoron
Abstract & topological properties
Flag count	57600
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Flag orbits	4
Convex	No
Nature	Tame

The pentagrammal antiprismatoverted hexacosihecatonicosachoron, or papvixhi, is a nonconvex uniform polychoron that consists of 120 great icosahedra and 600 truncated tetrahedra. 2 great icosahedra and 10 truncated tetrahedra join at each vertex.

Vertex coordinates

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

Gallery

External links

• Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#90).

• Klitzing, Richard. "papvixhi".