This is the great icosahedron, which is one of the Kepler-Poinsot solids.

All twenty of the faces of the great icosahedron are equilateral triangles. They interpenetrate, so they can be a little difficult to see. Here’s a still view, with one face highlighted.

If each of these twenty faces is augmented by a regular triangular antiprism (also known as the Platonic octahedron), here is the result — a variant of the Platonic icosahedron.

I also tried augmenting the great icosahedron with prisms, and this is the result — a variant of the Archimedean icosidodecahedron.

I made these images using Stella 4d: Polyhedron Navigator, which you can try for free at this website.