Icosahedral bipyramid

Orthogonal projection
Central icosahedron with 30 blue edges and 20 red vertices, apex vertices in yellow, connecting to icosahedron with 24 black edges.
Type  | Polyhedral bipyramid
Schläfli symbol | {3,5} + { }
dt{2,5,3}
Coxeter-Dynkin  |
Cells  | 40 {3,3}
Faces  | 80 {3}
Edges  | 54 (30+12+12)
Vertices  | 14 (12+2)
Dual  | Dodecahedral prism
Symmetry group | [2,3,5], order 240
Properties  | convex, regular-celled, Blind polytope

In 4-dimensional geometry, the icosahedral bipyramid is the direct sum of a icosahedron and a segment, {3,5} + { }. Each face of a central icosahedron is attached with two tetrahedra, creating 40 tetrahedral cells, 80 triangular faces, 54 edges, and 14 vertices.[1] An icosahedral bipyramid can be seen as two icosahedral pyramids augmented together at their bases.

It is the dual of a dodecahedral prism, Coxeter-Dynkin diagram , so the bipyramid can be described as . Both have Coxeter notation symmetry [2,3,5], order 240.

Having all regular cells (tetrahedra), it is a Blind polytope.

## See also

* Pentagonal bipyramid \- A lower dimensional analogy
* Tetrahedral bipyramid
* Octahedral bipyramid \- A lower symmetry form of the as 16-cell.
* Cubic bipyramid
* Dodecahedral bipyramid

## References

1. ↑ "Ite". https://www.bendwavy.org/klitzing/incmats/ikedpy.htm.

* Klitzing, Richard, "Johnson solids, Blind polytopes, and CRFs", Polytopes, https://bendwavy.org/klitzing/explain/johnson.htm, retrieved 2022-11-14

## External links

* Icosahedral tegum

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