This model is an "augmentation" of a truncated dodecahedron. On three decagonal faces, the decagon serves as the base of a figure with a regular pentagon on top and five square and five triangular sides. The faces of the model total of thirty-five equilateral triangles faces, fifteen squares, three regular pentagons, and nine regular decagons.
On Berman's models of regular-faced convex polyhedra, see 1978.1065.01.