Pseudorhombic small hecatonicosihexacosichoron

Pseudorhombic small hecatonicosihexacosichoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Pirshix
Elements
Cells	720 pentagonal prisms, 600 truncated octahedra, 120 truncated icosahedra
Faces	3600 squares, 1440 pentagons, 1200+2400 hexagons
Edges	3600+7200
Vertices	3600
Vertex figure	Isosceles triangular retroprism, edge lengths √2 (4), (1+√5)/2 (2), and √3 (6)
Measures (edge length 1)
Circumradius	${\sqrt {7+2{\sqrt {5}}}}\approx 3.38705$
Hypervolume	$15{\frac {1065+467{\sqrt {5}}}{4}}\approx 7909.66405$
Dichoral angles	Toe–6–toe: $\arccos \left({\frac {1-3{\sqrt {5}}}{8}}\right)\approx 135.52249^{\circ }$
	Ti–6–toe: $\arccos \left({\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 22.23876^{\circ }$
	Ti–5–pip: 18°
	Toe–4–pip: $\arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{10}}}\right)\approx 13.28253^{\circ }$
Related polytopes
Army	Semi-uniform srix
Regiment	Sirghi
Conjugate	Pseudorhombic great hecatonicosihexacosichoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The pseudorhombic small hecatonicosihexacosichoron, or pirshix, is a nonconvex uniform polychoron that consists of 120 truncated icosahedra, 720 pentagonal prisms, and 600 truncated octahedra. Two truncated icosahedra, two pentagonal 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 great hecatonicosachoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#189).