Faceted rectified great stellated hecatonicosachoron

Faceted rectified great stellated hecatonicosachoron
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Frogshi
Elements
Cells	120 did, 120 quit sissid
Faces	1440 pentagons, 720 pentagrams, 720 decagrams
Edges	3600
Vertices	720
Vertex figure	Pentagrammic toroprism
Measures (edge length 1)
Circumradius	$\sqrt{\frac{5-\sqrt5}{2}} \approx 1.17557$
Number of pieces	137040
Level of complexity	353
Related polytopes
Army	Rox
Regiment	Ragishi
Conjugate	Ridhi
Convex core	Hecatonicosachoron
Abstract properties
Euler characteristic	–240
Topological properties
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The faceted rectified great stellated hecatonicosachoron, or frogshi, also known as the facetorectified great stellated hecatonicosachoron, is a nonconvex uniform polychoron that consists of 120 dodecadodecahedra and 120 quasitruncated small stellated dodecahedra. Five dodecadodecahedra and ten quasitruncated small stellated dodecahedra join at each vertex.

It also has great dodecahedra and great dodecahemidodecahedra as pseudofacets.

Gallery

Vertex coordinates

The vertices are the same as those of the regiment colonel, the rectified great stellated hecatonicosachoron.

External links

• Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#107).