Icosahedral prism

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.

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

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 - ${\displaystyle s\left\{{\begin{array}{l}3\\3\\2\end{array}}\right\}}$ = ht_0,1,2,3{3,3,2} or , a related nonuniform 4-polytope

External links

• 6. Convex uniform prismatic polychora - Model 59, George Olshevsky.
• Klitzing, Richard. "4D uniform polytopes (polychora) x o3o5x - ipe".