 | ||
The icosahedral pyramid is a four-dimensional convex polytope, bounded by one icosahedron as its base and by 20 triangular pyramid cells which meet at its apex. Since an icosahedron has a circumradius divided by edge length less than one, the tetrahedral pyramids can be made with regular faces.
The regular 600-cell has icosahedral pyramids around every vertex.
The dual to the icosahedral pyramid is the dodecahedral pyramid, seen as a dodecahedral base, and 20 regular pentagonal pyramids meeting at an apex.
References
Icosahedral pyramid Wikipedia(Text) CC BY-SA