Hecatonicosintercepted prismatohecatonicosihexacosichoron

Hecatonicosintercepted prismatohecatonicosihexacosichoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Hin phix
Elements
Cells	720 pentagrammic prisms, 600 octahemioctahedra, 120 great icosidodecahedra, 120 great quasitruncated icosidodecahedra
Faces	1200+2400 triangles, 3600 squares, 1440 pentagrams, 2400 hexagons, 720 decagrams
Edges	3600+7200
Vertices	3600
Vertex figure	Windowed wedge, edge lengths 1 (3) √2 (4), (√5–1)/2 (2), √3 (4), √(5–√5)/2 (2)
Measures (edge length 1)
Circumradius	${\sqrt {19-8{\sqrt {5}}}}\approx 1.05425$
Hypervolume	$5{\frac {2591{\sqrt {5}}-5730}{2}}\approx 159.13032$
Dichoral angles	Oho–6–gaquatid: $\arccos \left(-{\frac {\sqrt {10}}{4}}\right)\approx 142.23876^{\circ }$
	Gid–5/2–stip: 126°
	Gid–3–oho: $\arccos \left(-{\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 97.76124^{\circ }$
	Gaquatid–4–stip: $\arccos \left({\sqrt {\frac {5-{\sqrt {5}}}{10}}}\right)\approx 58.28253^{\circ }$
	Oho–3–oho: $\arccos \left({\frac {3{\sqrt {5}}-1}{8}}\right)\approx 44.47751^{\circ }$
	Gaquatid–10/3–gaaquatid: 36°
Related polytopes
Army	Semi-uniform srahi
Regiment	Sirgax
Conjugate	Hecaatonicosintercepted prismatohexacosihecatonicosachoron
Abstract & topological properties
Euler characteristic	3000
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The hecatonicosintercepted prismatohecatonicosihexacosichoron, or hin phix, is a nonconvex uniform polychoron that consists of 120 great icosidodecahedra, 600 octahemioctahedra, 720 pentagrammic prisms, and 120 great quasitruncated icosidodecahedra. One great icosidodecahedron, two octahemioctahedra, two pentagrammic prisms, and four great quasitruncated icosidodecahedra join at each vertex.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#220).