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
- Icosahedral dyadic prism Norman W. Johnson
- Ipe for icosahedral prism/hyperprism (Jonathan Bowers)
- Snub tetrahedral prism/hyperprism
Related polytopes
- Snub tetrahedral antiprism - = ht0,1,2,3{3,3,2} or
gollark: PotatOS's string metatable bug implementation has high latency and does only store whatever can be serialized to JSÖN, but I think it's quite good.
gollark: Utilizing my reimplementation of the string metatable bug for shared storage of all transactions and data, it requires full trust in every participant.
gollark: Nope!
gollark: We should just switch to Potato Transact\™.
gollark: The shell script, when run, writes GCC out to a temporary file, writes out your code, compiles it with optimization at minimum and executes it.
External links
- 6. Convex uniform prismatic polychora - Model 59, George Olshevsky.
- Klitzing, Richard. "4D uniform polytopes (polychora) x o3o5x - ipe".
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.