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)
TypePolyhedral bipyramid
Schläfli symbol{3,5} { }
dt{2,5,3}
Coxeter diagram
Cells40 {3,3}
Faces80 {3}
Edges54 (30 12 12)
Vertices14 (12 2)
Symmetry group[2,3,5], order 240
Propertiesconvex, 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

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References

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  1. ^ "Ite".
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