# Pseudorhombic prismatopentachoron

Pseudorhombic prismatopentachoron
Rank4
TypeUniform
Notation
Bowers style acronymPirpop
Elements
Cells10 triangular prisms, 10 hexagonal prisms, 5 truncated tetrahedra
Faces20 triangles, 15+30 squares, 20 hexagons
Edges30+60
Vertices30
Vertex figureIsosceles triangular retroprism, edge lengths 1 (2), 2 (6), and 3 (4)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {35}}{5}}\approx 1.18632}$
Hypervolume${\displaystyle {\frac {89{\sqrt {5}}}{96}}\approx 2.07302}$
Dichoral anglesTut–3–trip: ${\displaystyle \arccos \left(-{\frac {\sqrt {6}}{4}}\right)\approx 52.23876^{\circ }}$
Tut–6–hip: ${\displaystyle \arccos \left(-{\frac {\sqrt {6}}{4}}\right)\approx 52.23876^{\circ }}$
Trip–4–hip: ${\displaystyle \arccos \left({\frac {2}{3}}\right)\approx 48.18968^{\circ }}$
Hip–4–hip: ${\displaystyle \arccos \left({\frac {2}{3}}\right)\approx 48.18968^{\circ }}$
Related polytopes
ArmySrip
RegimentSrip
ConjugateNone
Convex corePentachoron
Abstract & topological properties
Flag count1440
Euler characteristic0
OrientableYes
Properties
SymmetryA4, order 120
ConvexNo
NatureTame

The pseudorhombic prismatopentachoron, or pirpop, is a nonconvex uniform polychoron that consists of 5 truncated tetrahedra, 10 triangular prisms, and 10 hexagonal prisms. 2 truncated tetrahedra, 2 triangular prisms and 4 hexagonal prisms join at each vertex.

## Vertex coordinates

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