Prismatopentintercepted dispentachoron

Prismatopentintercepted dispentachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Pippindip
Elements
Cells	5 octahedra, 10 hexagonal prisms, 5 truncated tetrahedra, 5 cuboctahedra
Faces	10+20+20 triangles, 15+30 squares, 20 hexagons
Edges	30+60
Vertices	30
Vertex figure	Inverted wedge, edge lengths 1 (5), √2 (6), and √3 (4)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {35}}{5}}\approx 1.18632$
Hypervolume	${\frac {235{\sqrt {5}}}{96}}\approx 5.47371$
Dichoral angles	Co–3-oct: $\arccos \left(-{\frac {1}{4}}\right)\approx 104.47751^{\circ }$
	Oct–3–tut: $\arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }$
	Co–3–co: $\arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }$
	Co–4–hip: $\arccos \left({\frac {\sqrt {6}}{6}}\right)\approx 65.90516^{\circ }$
	Tut–6–hip: $\arccos \left({\frac {\sqrt {6}}{4}}\right)\approx 52.23876^{\circ }$
	Hip–4–hip: $\arccos \left({\frac {2}{3}}\right)\approx 48.18968^{\circ }$
Related polytopes
Army	Srip
Regiment	Srip
Conjugate	None
Convex core	Pentachoron
Abstract & topological properties
Flag count	1800
Euler characteristic	30
Orientable	Yes
Properties
Symmetry	A4, order 120
Convex	No
Nature	Wild

The prismatopentintercepted dispentachoron, or pippindip, is a nonconvex uniform polychoron that consists of 5 truncated tetrahedra, 5 octahedra, 5 cuboctahedra, and 10 hexagonal prisms. 2 truncated tetrahedra, 2 cuboctahedra, 1 octahedron, and 4 hexagonal prisms join at each vertex.

It has the same faces as the prismatointercepted prismatodispentachoron.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#138).

• Klitzing, Richard. "pippindip".