The faces of this model are seven regular pentagons, fifteen equilateral triangles, and fifteen squares. The top and bottom are pentagons. Five triangles are around the top pentagon. Five pentagons and five triangles are in the ring below this. The next ring has ten squares, and the lowest (adjacent to the bottom pentagon) five triangles.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.