# Prismatointercepted prismatodispentachoron

Prismatointercepted prismatodispentachoron
Rank4
TypeUniform
Notation
Bowers style acronymPinnipdip
Elements
Cells10 triangular prisms, 5 octahedra, 10 hexagonal prisms, 5 octahemioctahedra
Faces10+20+20 triangles, 15+30 squares, 20 hexagons
Edges30+60
Vertices30
Vertex figureWindowed wedge, edge lengths 1 (5), 2 (6), and 3 (4)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {35}}{5}}\approx 1.18632}$
Hypervolume${\displaystyle {\frac {21{\sqrt {5}}}{16}}\approx 2.93484}$
Dichoral anglesOct–3–trip: ${\displaystyle \arccos \left(-{\frac {\sqrt {6}}{4}}\right)\approx 127.76124^{\circ }}$
Oho–3-oct: ${\displaystyle \arccos \left(-{\frac {1}{4}}\right)\approx 104.47751^{\circ }}$
Oho–3–oho: ${\displaystyle \arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }}$
Oho–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 coreJoined pentachoron
Abstract & topological properties
Flag count1800
Euler characteristic25
OrientableYes
Properties
SymmetryA4, order 120
ConvexNo
NatureWild

The prismatointercepted prismatodispentachoron, or pinnipdip, is a nonconvex uniform polychoron that consists of 5 octahedra, 5 octahemioctahedra, 10 triangular prisms, and 10 hexagonal prisms. 1 octahedron, 2 octahemioctahedra, 2 triangular prisms, and 4 hexagonal prisms join at each vertex.

It has the same faces as the prismatopentintercepted dispentachoron.

## Vertex coordinates

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