Pseudorhombic great hecatonicosihexacosichoron

Pseudorhombic great hecatonicosihexacosichoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Pirghix
Elements
Cells	720 pentagrammic prisms, 600 truncated octahedra, 120 truncated great icosahedra
Faces	3600 squares, 1440 pentagrams, 1200+2400 hexagons
Edges	3600+7200
Vertices	3600
Vertex figure	Isosceles triangular retroprism, dege lengths √2 (4), (√5–1)/2 (2), and √3 (6)
Measures (edge length 1)
Circumradius	${\sqrt {7-2{\sqrt {5}}}}\approx 1.58993$
Hypervolume	$15{\frac {1065-467{\sqrt {5}}}{4}}\approx 77.83595$
Dichoral angles	Tiggy–5/2–stip: 126°
	Tiggy–6–toe: $\arccos \left({\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 82.23876^{\circ }$
	Toe–4–stip: $\arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{10}}}\right)\approx 66.71747^{\circ }$
	Toe–6–toe: $\arccos \left({\frac {1+3{\sqrt {5}}}{8}}\right)\approx 15.52249^{\circ }$
Related polytopes
Army	Srahi
Regiment	Sirgashi
Conjugate	Pseudorhombic small hecatonicosihexacosichoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The pseudorhombic great hecatonicosihexacosichoron, or pirghix, is a nonconvex uniform polychoron that consists of 120 truncated great icosahedra, 720 pentagrammic prisms, and 600 truncated octahedra. Two truncated great icosahedra, two pentagrammic prisms, and four truncated octahedra join at each vertex.

Vertex coordinates

The vertices are the same as those of the regiment colonel, the small rhombated grand stellated hecatonicosachoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#210).