Great polar facetopental trishecatonicosachoron

Great polar facetopental trishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gliffipathi
Elements
Cells	120 qrid, 120 gid, 120 quit gissid
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	100080
Level of complexity	232
Related polytopes
Army	Rox
Regiment	Rigfix
Conjugate	Sofapathi
Convex core	Hecatonicosachoron
Abstract & topological properties
Euler characteristic	4320
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The great polar facetopental trishecatonicosachoron, or gliffipathi, is a nonconvex uniform polychoron that consists of 120 quasirhombicosidodecahedra, 120 great icosidodecahedra, and 120 quasitruncated great stellated dodecahedra. Ten quasirhombicosidodecahedra, five great icosidodecahedra, and ten quasitruncated great stellated dodecahedra join at each vertex.

It also has great complex icosidodecahedra 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" (#126).