Faceted rectified hexacosichoron

Faceted rectified hexacosichoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Frox
Coxeter diagram	x3o3/2x5o -600 2thah
Elements
Cells	120 id, 720 pip
Faces	1200 triangles, 1800 squares, 1440 pentagons
Edges	3600
Vertices	720
Vertex figure	Pentagrammic toroprism
Edge figure	id.id.pip.pip.pip
Measures (edge length 1)
Circumradius	${\sqrt {5+2{\sqrt {5}}}}\approx 3.07768$
Hypervolume	${\frac {200+75{\sqrt {5}}}{2}}\approx 183.85255$
Number of external pieces	40680
Level of complexity	80
Related polytopes
Army	Rox
Regiment	Rox
Conjugate	Retroinverted prismatohecatonicosachoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Euler characteristic	720
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The faceted rectified hexacosichoron, or frox, is a nonconvex uniform polychoron that consists of 120 icosidodecahedra and 720 pentagonal prisms. 5 icosidodecahedra and 10 pentagonal prisms join at each vertex.

It is in the regiment of the rectified hexacosichoron.

Gallery

External links

• Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#77).

• Klitzing, Richard. "frox".