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's circumradius is less than its edge length,[1] the tetrahedral pyramids can be made with regular faces.
Two copies can be augmented to make an icosahedral bipyramid which is also a Blind Polytope.
The regular 600-cell has icosahedral pyramids around every vertex.
Seen in a configuration matrix, all incidence counts between elements are shown.