[math-fun] Dodecahedron dissection

Problem: dissect into tetrahedra the regular dodecahedron with interior, so that the resulting complex is symmetric under reflection in its centre. I have a solution with 20 vertices, 61 edges, 66 triangles, 24 tetrahedra: can any of these counts be reduced? [ Further details concerning this solution, and the motivation behind the problem, available on demand. ] Fred Lunnon