Codes in platonic, Archimedean, Catalan, and related polyhedra: a model for maximum addition patterns in chemical cages.
The notion of d-code is extended to general polyhedra by defining maximum sets of vertices with pairwise separation > or =d. Codes are enumerated and classified by symmetry for all regular and semiregular polyhedra and their duals. Partial results are also given for the series of medials of Archimedean polyhedra. In chemistry, d-codes give a model for maximal addition to or substitution in polyhedral frameworks by bulky groups. Some illustrative applications from the chemistry of fullerenes and boranes are described.
School of Chemistry, University of Exeter, Stocker Road, Exeter EX4 4QD, UK.
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de La Vaissière
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Fowler
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Deza