Prismatointercepted prismatohexacosihecatonicosachoron

Prismatointercepted prismatohexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Pinpixhi
Elements
Cells	1200 triangular prisms, 600 octahedra, 720 decagonal prisms, 120 small dodecicosidodecahedra
Faces	2400+2400 triangles, 1800+3600 squares, 720 pentagons, 1440 decagons
Edges	3600+7200
Vertices	3600
Vertex figure	Windowed wedge, edge lengths 1 (4), √2 (6), (1+√5)/2 (1), and √(5+√5)/2 (4)
Measures (edge length 1)
Circumradius	${\sqrt {23+10{\sqrt {5}}}}\approx 6.73503$
Hypervolume	$5{\frac {3680+1723{\sqrt {5}}}{2}}\approx 18681.8628$
Dichoral angles	Oct–3–trip: $\arccos \left(-{\frac {{\sqrt {6}}+{\sqrt {30}}}{8}}\right)\approx 172.23876^{\circ }$
	Saddid–10–dip: 162°
	Saddid–3–oct: $\arccos \left(-{\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 157.76124^{\circ }$
	Dip–4–dip: $\arccos \left(-{\frac {2{\sqrt {5}}}{5}}\right)\approx 153.43495^{\circ }$
	Saddid–5–saddid: 144°
	Dip–4–trip: $\arccos \left({\sqrt {\frac {10+2{\sqrt {5}}}{15}}}\right)\approx 10.81232^{\circ }$
Related polytopes
Army	Srahi
Regiment	Srahi
Conjugate	Disprismatointercepted hexacosihecatonicosachoron
Convex core	Chamfered hecatonicosachoron
Abstract & topological properties
Euler characteristic	2520
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The prismatointercepted prismatohexacosihecatonicosachoron is a nonconvex uniform polychoron that consists of 600 octahedra, 120 small dodecicosidodecahedra, 1200 triangular prisms, and 720 decagonal prisms. One octahedron, two small dodecicosidodecahedra, two triangular prisms, 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" (#164).

• Klitzing, Richard. "pinpixhi".