This model has a regular pentagon on the top, a round of five equilateral triangles, a round of five regular pentagons and five equilateral triangles, a round of ten squares, and a regular decagon on the bottom. Hence its faces total of six regular pentagons, ten equilateral triangles, ten squares, and a regular decagon.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.