As well as the 21 instances of the Platonic solids of the first four types, some of the vertices of the disdyakis triacontahedron are vertices of a dodecahedron, five rhombic dodecahedra and one rhombic triacontahedron (either Platonic or Catalan solids), as well as an icosidodecahedron (not shown above), an Archimedean solid that is the dual of the rhombic triacontahedron (see #9).

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