Hecatonicosintercepted prismatohexacosihecatonicosachoron

Hecatonicosintercepted prismatohexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Hinpixhi
Elements
Cells	720 pentagonal prisms, 600 octahemioctahedra, 120 icosidodecahedra, 120 great rhombicosidodecahedra
Faces	1200+2400 triangles, 3600 squares, 1440 pentagons, 2400 hexagons, 720 decagons
Edges	3600+7200
Vertices	3600
Vertex figure	Windowed wedge, edge lengths 1 (3), √2 (4), (1+√5)/2 (2), √3 (4), and √(5+√5)/2
Measures (edge length 1)
Circumradius	${\sqrt {19+8{\sqrt {5}}}}\approx 6.07359$
Hypervolume	$5{\frac {5730+2591{\sqrt {5}}}{2}}\approx 28809.1303$
Dichoral angles	Oho–3–oho: $\arccos \left(-{\frac {1+3{\sqrt {5}}}{8}}\right)\approx 164.47751^{\circ }$
	Id–5–pip: 162°
	Id–3–oho: $\arccos \left(-{\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 157.76124^{\circ }$
	Oho–6–grid: $\arccos \left(-{\frac {\sqrt {10}}{4}}\right)\approx 142.23876^{\circ }$
	Grid–10–grid: 108°
	Grid–4–pip: $\arccos \left({\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)\approx 31.71747^{\circ }$
Related polytopes
Army	Srix
Regiment	Srix
Conjugate	Hecatonicosintercepted prismatohecatonicosihexacosichoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Euler characteristic	3000
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The hecatonicosintercepted prismatohexacosihecatonicosachoron, or hinpixhi, is a nonconvex uniform polychoron that consists of 120 icosidodecahedra, 600 octahemioctahedra, 720 pentagonal prisms, and 120 great rhombicosidodecahedra. One icosidodecahedron, two octahemioctahedra, two pentagonal prisms, and four great rhombicosidodecahedra join at each vertex.

Vertex coordinates

The vertices are the same as those of the regiment colonel, the small rhombated hexacosichoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#171).