Pentakis Dodecahedron Puzzle

The 60 faces of a Pentakis Dodecahedron are isosceles triangles. Choose one out of four possible positions at each side of the triangles: R=right from center, RR=far right from center, L=left from center or LL=far left from center. With gaps at the chosen positions you can get 4x4x4=64 different triangles. If the pieces with same chosen positions at each side are discarded 60 pieces are left just enough to construct the Pentakis Dodecahedron with L-R and LL-RR matching edges.