Pentagrammal antiprismatoverted hexacosihecatonicosachoron

Pentagrammal antiprismatoverted hexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Papvixhi
Coxeter diagram	(o3x3x3o5/2*a)/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	$\sqrt{\frac{5+\sqrt5}{2}} ≈ 1.90211$
Hypervolume	$25\frac{51+22\sqrt5}{4} ≈ 626.20935$
Dichoral angles	Tut–6–tut: $\arccos\left(-\frac{1+3\sqrt5}{8}\right) ≈ 164.47751°$
	Gike–3–tut: $\arccos\left(-\frac{\sqrt{7+3\sqrt5}}{4}\right) ≈ 157.76124°$
Central density	17
Number of external pieces	32520
Level of complexity	86
Related polytopes
Army	Rox
Regiment	Righi
Conjugate	Pentagonal retroprismatoverted hexacosihecatonicosachoron
Convex core	Hexacosichoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
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".