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The dodecahedron is the last Platonic solid, and can be derived from the icosahedron by replacing each of its corners with a pentagon such that neighboring pentagons share edges. As it has 20 vertices and 12 faces, a dodecahedron of atoms would enclose a large amount of space, making it a rare coordination environment for single atoms. Remarkable exceptions are the intermetallic clathrates. In intermetallic structures, dodecahedral shells can arise around groups of atoms, such as tetrahedra or icosahedra.