The best coloration I found for this one is to use 20 modules each of three colors. Take color 1 and make the top and bottom pentagons. Take color 2, and complete the triangles around each of these pentagons. This will take all 20 modules of color 2. Take color 3, and form the two edges of the remaining triangles that attach to the triangles of color 2. This will take all 20 modules of color 3. The remaining 10 modules of color 1 form a decagonal band around the middle of the polyhedron, attaching the two halves you have just created.
It is also possible to divide the edges of this polyhedron into six decagonal bands. Unfortunately, it is hard to get six colors to look nice together.
