Icosahedral pyramid
| Icosahedral pyramid | ||
|---|---|---|
 Schlegel diagram | ||
| Type | Polyhedral pyramid | |
| Schläfli symbol | ( ) ∨ {3,5} | |
| Cells | 21 | 1 icosahedron  20 tetrahedra  |
| Faces | 50 | 20+30 {3} |
| Edges | 12+30 | |
| Vertices | 13 | |
| Dual | Dodecahedral pyramid | |
| Symmetry group | H3, [5,3,1], order 120 | |
| Properties | convex, regular-faces | |
In 4-dimensional geometry, the icosahedral pyramid is bounded by one icosahedron on the base and 20 triangular pyramid cells which meet at the apex. Since an icosahedron has a circumradius divided by edge length less than one,[1] the tetrahedral pyramids can made with regular faces.
The regular 600-cell has icosahedral pyramids around every vertex.
The dual to the icosahedral pyramid is a dodecahedral pyramid, seen as an dodecahedral base, and 20 regular pentagonal pyramid meeting at an apex.
References
- ↑ Richard Klitzing, 3D convex uniform polyhedra, x3o5o - ike, circumradius sqrt[(5+sqrt(5))/8 = 0.951057
External links
- Olshevsky, George, Pyramid at Glossary for Hyperspace.
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Wikimedia Commons has media related to Pyramids (geometry). |
- Richard Klitzing, 4D, Segmentotopes
- Richard Klitzing, Segmentotope, ikepy, K-4.84
- Richard Klitzing, Axial-Symmetrical Edge Facetings of Uniform Polyhedra