Of the five Platonic Solids, the regular Dodecahedron and the Icosahedron do not appear in the structure of crystals. An irregular Dodecahedron structure is found in Pyritohedron minerals, and many viruses have Icosahedral structures. Plato remarked that

God used the Dodecahedron ‘for arranging constellations on the whole heaven’.

Including: Dodecahedrons and Icosahedrons (Platonic), and a Truncated Icosahedron (Archimides).