New perspectives on polyhedral molecules and their crystal structures

Relevant families of ideal polyhedra (Platonic, Archimedean, prisms, Johnson, and Fullerenes) are briefly summarized, and an overview of polyhedral alkanes and alkenes, existing or hypothetical, is presented. The assignment of a polyhedral shape to a specific compound with the help of continuous shape measures and derived tools is also briefly discussed, and application of shape analysis to cyclic molecules such as cyclobutane, cyclohexane, and cyclooctatetraene is presented to illustrate the usefulness of ideal polyhedra in the stereochemical description of non‐polyhedral molecules. Finally, the presence of latent octahedral symmetry in icosahedral polyhedra is used to design new molecules with nested shells of the two supposedly incompatible symmetries, and to explain the cubic crystal structures of icosahedral molecules such as dodecahedrane and Buckminsterfullerene.