Icosahedral prism

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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 CDel node 1.pngCDel 3.pngCDel node.pngCDel 5.pngCDel node.pngCDel 2.pngCDel node 1.png
CDel node h.pngCDel 3.pngCDel node h.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.png
CDel node h.pngCDel 3.pngCDel node h.pngCDel 3.pngCDel node h.pngCDel 2.pngCDel node 1.png
Cells 2 (3.3.3.3.3)Icosahedron.png
20 (3.4.4)Triangular prism.png
Faces 30 {4}
40 {3}
Edges 72
Vertices 24
Vertex figure Snub tetrahedral prism verf.png
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.

Icosahedral prism net.png
Net
Icosahedral prism.png
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 - = ht0,1,2,3{3,3,2} or CDel node h.pngCDel 3.pngCDel node h.pngCDel 3.pngCDel node h.pngCDel 2x.pngCDel node h.png, 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".
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