| Icosahedral prism | |
|---|---|
Schlegel diagram Only one icosahedral cell shown |
|
| Type | Prismatic uniform polychoron |
| Uniform index | 59 |
| Schläfli symbol | {3,5}x{} h0,1{3,4}x{} s{3,3}x{} |
| Coxeter-Dynkin | |
| Cells | 2 (3.3.3.3.3) 20 (3.4.4) |
| Faces | 30 {4} 40 {3} |
| Edges | 72 |
| Vertices | 24 |
| Vertex configuration | 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 polychoron (four dimensional polytope). This polychoron 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.
Alternative names:
It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of parallel Platonic solids or Archimedean solids.