Icosahedral bipyramid

In 4-dimensional geometry, the icosahedral bipyramid is the direct sum of an 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.

Icosahedral bipyramid
Orthogonal projection:   Base icosahedron edges (30)   Base icosahedron vertices (12)   Apex vertices (2)   Connecting edges (24)
Type	Polyhedral bipyramid
Schläfli symbol	{3,5} + { } dt{2,5,3}
Coxeter diagram
Cells	40 {3,3}
Faces	80 {3}
Edges	54 (30+12+12)
Vertices	14 (12+2)
Symmetry group	[2,3,5], order 240
Properties	convex, regular-celled, Blind polytope

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