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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.

Richard Klitzing, 4D, Segmentotopes
Richard Klitzing, Segmentotope, ikepy, K-4.84
Richard Klitzing, Axial-Symmetrical Edge Facetings of Uniform Polyhedra

Mathematics Encyclopedia

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