# Prismatointercepted pentachoron

Prismatointercepted pentachoron
Rank4
TypeUniform
Notation
Bowers style acronymPinnip
Elements
Cells
Faces10+20 triangles, 15 squares
Edges30
Vertices10
Vertex figureTriangular toroprism, edge lengths 1 (edges of squares) and 2 (long edges of triangles)
Edge figureoct 3 oct 3 trip 4 trip 4 trip 3
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {15}}{5}}\approx 0.77460}$
Hypervolume${\displaystyle {\frac {7{\sqrt {5}}}{48}}\approx 0.32609}$
Dichoral angleOct–3–oct: ${\displaystyle \arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }}$
Oct–3–trip: ${\displaystyle \arccos \left({\frac {\sqrt {6}}{4}}\right)\approx 52.23876^{\circ }}$
Trip–4–trip: ${\displaystyle \arccos \left({\frac {2}{3}}\right)\approx 48.18968^{\circ }}$
Number of external pieces25
Level of complexity6
Related polytopes
ArmyRap
RegimentRap
ConjugateNone
Convex coreJoined pentachoron
Abstract & topological properties
Flag count600
Euler characteristic10
OrientableYes
Properties
SymmetryA4, order 120
Flag orbits5
ConvexNo
NatureWild

The prismatointercepted pentachoron, or pinnip, is a nonconvex uniform polychoron that consists of 5 regular octahedra and 10 triangular prisms. 3 octahedra and 6 triangular prisms join at each vertex.

It is the simplest wild uniform polytope. It is wild because it has octahedra with squares intercepting them.

## Vertex coordinates

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