# Icosahedral prism

Icosahedral prism
Type Prismatic uniform 4-polytope
Uniform index 59
Schläfli symbol t0,3{3,5,2} or {3,5}×{}
s{3,4}×{}
sr{3,3}×{}
Coxeter-Dynkin

Cells 2 (3.3.3.3.3)
20 (3.4.4)
Faces 30 {4}
40 {3}
Edges 72
Vertices 24
Vertex figure
Regular-pentagonal pyramid
Symmetry group [5,3,2], order 240
[3+,4,2], order 48
[(3,3)+,2], order 24
Properties convex

In geometry, an icosahedral prism is a convex uniform 4-polytope (four-dimensional polytope). This 4-polytope has 22 polyhedral cells: 2 icosahedra connected by 20 triangular prisms. It has 70 faces: 30 squares and 40 triangles. It has 72 edges and 24 vertices.

It can be constructed by creating two coinciding icosahedra in 3-space, and translating each copy in opposite perpendicular directions in 4-space until their separation equals their edge length.

It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of parallel Platonic solids or Archimedean solids.

 Net Schlegel diagram Only one icosahedral cell shown

## Alternate names

1. Icosahedral dyadic prism Norman W. Johnson
2. Ipe for icosahedral prism/hyperprism (Jonathan Bowers)
3. Snub tetrahedral prism/hyperprism

## Related polytopes

• Snub tetrahedral antiprism - ${\displaystyle s\left\{{\begin{array}{l}3\\3\\2\end{array}}\right\}}$ = ht0,1,2,3{3,3,2} or , a related nonuniform 4-polytope