Icosahedral bipyramid

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. 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

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

External links

• Icosahedral tegum