Omnicircumfacetopental hexacosidishecatonicosachoron

Omnicircumfacetopental hexacosidishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Omfapaxady
Elements
Cells	120 sissid, 600 oct, 120 gaddid
Faces	3600 triangles, 1440 pentagrams, 720 decagrams
Edges	3600
Vertices	720
Measures (edge length 1)
Circumradius	$\sqrt{5-2\sqrt5} \approx 0.72654$
Number of external pieces	87840
Level of complexity	236
Related polytopes
Army	Rox
Regiment	Rigfix
Conjugate	Ipixady
Convex core	Hecatonicosachoron
Abstract & topological properties
Euler characteristic	2040
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The omnicircumfacetopental hexacosidishecatonicosachoron, or omfapaxady, is a nonconvex uniform polychoron that consists of 120 small stellated dodecahedra, 600 octahedra, and 120 great dodecicosidodecahedra. Two small stellated dodecahedra, five octahedra, and ten great dodecicosidodecahedra join at each vertex.

It also has 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" (#128).

• Klitzing, Richard. "omfapaxady".