Prismatohecatonicosintercepted hexacosihecatonicosachoron

Prismatohecatonicosintercepted hexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Phinxhi
Elements
Cells	600 octahedra, 720 decagonal prisms, 120 truncated dodecahedra, 120 small rhombicosidodecahedra
Faces	2400+2400 triangles, 1800+3600 squares, 720 pentagons, 1440 decagons
Edges	3600+7200
Vertices	3600
Vertex figure	Inverted wedge, edge lengths 1 (4), √2 (6), (1+√5)/2 (1), and (1+√5)/2 (4)
Measures (edge length 1)
Circumradius	${\sqrt {23+10{\sqrt {5}}}}\approx 6.73503$
Hypervolume	$5{\frac {13135+5881{\sqrt {5}}}{4}}\approx 32856.6447$
Dichoral angles	Srid–3–oct: $\arccos \left(-{\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 157.76124^{\circ }$
	Dip–4–dip: $\arccos \left(-{\frac {2{\sqrt {5}}}{5}}\right)\approx 153.43495^{\circ }$
	Srid–4–dip: $\arccos \left(-{\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)\approx 148.28253^{\circ }$
	Srid–5–srid: 144°
	Oct–3–tid: $\arccos \left({\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 22.23876^{\circ }$
	Tid–10–dip: 18°
Central density	0
Related polytopes
Army	Srahi
Regiment	Srahi
Conjugate	Prismatointercepted hexacosidishecatonicosachoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Euler characteristic	3600
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The prismatohecatonicosintercepted hexacosihecatonicosachoron, or phinxhi, is a nonconvex uniform polychoron that consists of 600 octahedra, 120 small rhombicosidodecahedra, 120 truncated dodecahedra, and 720 decagonal prisms. One octahedron, two small rhombicosidodecahedra, two truncated dodecahedra, and four decagonal prisms join at each vertex.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#163).