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 | |
|---|---|
 | |
| 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
edit- Pentagonal bipyramid - A lower dimensional analogy
- Tetrahedral bipyramid
- Octahedral bipyramid - A lower symmetry form of the as 16-cell.
- Cubic bipyramid
- Dodecahedral bipyramid
References
edit- Klitzing, Richard, "Johnson solids, Blind polytopes, and CRFs", Polytopes, retrieved 2022-11-14
External links
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