Icosahedral prism

Summary

Icosahedral prism
Type Prismatic uniform 4-polytope
Uniform index 59
Schläfli symbol t{2,3,5} 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
pentagonal pyramids
Dual Dodecahedral bipyramid
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

Orthographic projection

Alternate names edit

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

Related polytopes edit

  • Snub tetrahedral antiprism -   = ht0,1,2,3{3,3,2} or        , a related nonuniform 4-polytope

External links edit

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