Faceted rectified great grand hecatonicosachoron

Faceted rectified great grand hecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Firgaghi
Coxeter diagram	(x3x5/2o3o5/3*a)/2 (/2)
Elements
Cells	120 great stellated dodecahedra 120 truncated great icosahedra
Faces	1440 pentagrams 1200 hexagons
Edges	3600
Vertices	1200
Vertex figure	Triangular retroprism, edge lengths (√5–1)/2 (base) and √3 (sides)
Edge figure	gissid 5/2 tiggy 6 tiggy 6 tiggy 5/2
Measures (edge length 1)
Circumradius	${\frac {{\sqrt {15}}-{\sqrt {3}}}{2}}\approx 1.07047$
Hypervolume	$15{\frac {110-47{\sqrt {5}}}{2}}\approx 36.78604$
Dichoral angles	Gissid–5/2–tiggy: 72°
	Tiggy–6–tiggy: 60°
Central density	238
Number of external pieces	109320
Level of complexity	395
Related polytopes
Army	Rahi
Regiment	Ragaghi
Conjugate	Faceted rectified small stellated hecatonicosachoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Flag count	57600
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Flag orbits	4
Convex	No
Nature	Tame

The faceted rectified great grand hecatonicosachoron, or firgaghi, is a nonconvex uniform polychoron that consists of 120 great stellated dodecahedra and 120 truncated great icosahedra. Two great stellated dodecahedra and six truncated great icosahedra join at each vertex.

Gallery

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the rectified great grand hecatonicosachoron.

External links

• Bowers, Jonathan. "Category 3: Triangular Rectates" (#55).

• Klitzing, Richard. "firgaghi".