# Prismatointercepted pentachoron

(Redirected from Pinnip)
Prismatointercepted pentachoron
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymPinnip
Elements
Cells10 triangular prisms, 5 octahedra
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${\displaystyle \frac{\sqrt{15}}{5} ≈ 0.77460}$
Hypervolume${\displaystyle \frac{7\sqrt{5}}{48} ≈ 0.32609}$
Dichoral anglesOct–3–oct: ${\displaystyle \arccos\left(\frac14\right) ≈ 75.52249°}$
Oct–3–trip: ${\displaystyle \arccos\left(\frac{\sqrt6}{4}\right) ≈ 52.23876°}$
Trip–4–trip: ${\displaystyle \arccos\left(\frac23\right) ≈ 48.18968°}$
Number of pieces25
Level of complexity6
Related polytopes
ArmyRap
RegimentRap
ConjugateNone
Convex coreJoined pentachoron
Abstract properties
Euler characteristic10
Topological properties
OrientableYes
Properties
SymmetryA4, order 120
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.