Prismatotrispentachoron

Prismatotrispentachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Pittip
Coxeter diagram	x3x3x3/2o3*b ()
Elements
Cells	10 triangular prisms, 5 truncated tetrahedra, 5 octahemioctahedra, 5 truncated octahedra
Faces	20+20 triangles, 30 squares, 20+20 hexagons
Edges	30+60+60
Vertices	60
Vertex figure	skewed Bowtie pyramid, base edge lengths 1, √3, 1, √3; lateral edge lengths √2, √2, √3, √3
Measures (edge length 1)
Circumradius	${\frac {\sqrt {65}}{5}}\approx 1.61245$
Hypervolume	${\frac {419{\sqrt {5}}}{96}}\approx 9.75951$
Dichoral angles	Oho–3–trip: $\arccos \left(-{\frac {\sqrt {6}}{4}}\right)\approx 127.76125^{\circ }$
	Oho–3-tut: $\arccos \left(-{\frac {1}{4}}\right)\approx 104.47751^{\circ }$
	Oho–6–toe: $\arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }$
	Tut–6–toe: $\arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }$
	Toe–4–trip: $\arccos \left({\frac {\sqrt {6}}{6}}\right)\approx 65.90516^{\circ }$
Related polytopes
Army	Prip
Regiment	Prip
Conjugate	None
Abstract & topological properties
Flag count	1920
Euler characteristic	–5
Orientable	Yes
Properties
Symmetry	A4, order 120
Convex	No
Nature	Tame

The prismatotrispentachoron, or pittip, is a nonconvex uniform polychoron that consists of 10 triangular prisms, 5 truncated tetrahedra, 5 octahemioctahedra, and 5 truncated octahedra. 1 triangular prism, 1 truncated tetrahedron, 1 octahemioctahedron, and 2 truncated octahedra join at each vertex.

Cross-sections

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the prismatorhombated pentachoron.

External links

• Bowers, Jonathan. "Category 10: Prismatorhombates" (#353).

• Klitzing, Richard. "pittip".