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Space Filling Polyhedra A regular dodecahedron and this other unusual polyhedron (that I call "Anti-Dodecahedron" but George W. Hart call it "Concave Dodecahdron") can fill the space (use the same proportion of each ones). If you take into account their respective volumes, this means that dodecahdron alone can be close-packed with an efficiency ratio of more than 90.43% (which is not too bad, knowing that for spheres the maximum is supposed to be less than 74.05%).
This set contains only two ployhedra: one dodecaheron and one anti-dodecahedron. Order it several times to fill the whole space... :)