Omnifacetopental prismatohexacosihecatonicosachoron

Omnifacetopental prismatohexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Ofpipixhi
Elements
Cells	600 oct, 720 stip, 120 gaddid
Faces	3600 triangles, 1800 squares, 1440 pentagrams, 720 decagrams
Edges	3600
Vertices	720
Measures (edge length 1)
Circumradius	$\sqrt{5-2\sqrt5} \approx 0.72654$
Number of external pieces	253440
Level of complexity	628
Related polytopes
Army	Rox
Regiment	Rigfix
Conjugate	Lifpipixhi
Convex core	Joined hexacosichoron
Abstract & topological properties
Euler characteristic	3240
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The omnifacetopental prismatohexacosihecatonicosachoron, or ofpipixhi, is a nonconvex uniform polychoron that consists of 600 octahedra, 720 pentagrammic prisms, and 120 great dodecicosidodecahedra. Five octahedra, ten pentagrammic prisms, and ten great dodecicosidodecahedra join at each vertex.

It also has great complex icosidodecahedra and great icosidodecahedra+decagrams as exotic pseudofacets.

Gallery

Vertex coordinates

The vertices are the same as those of the regiment colonel, the rectified great faceted hexacosichoron.

External links

• Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#129).

• Klitzing, Richard. "ofpipixhi".