Icosahedral bipyramid explained

bgcolor=#e7dcc3 colspan=3	Icosahedral bipyramid
align=center colspan=3	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	+ dt
Coxeter-Dynkin
Cells
Faces	80
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, + . 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

External links

• Icosahedral tegum

Notes and References

1. Web site: Ite .