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Research Article

Codes in Platonic, Archimedean, Catalan, and Related Polyhedra: A Model for Maximum Addition Patterns in Chemical Cages

B. de La Vaissière,^† P. W. Fowler,*^† and M. Deza^‡

School of Chemistry, University of Exeter, Stocker Road, Exeter EX4 4QD, UK, and CNRS and DMI, Ecole Normale Suprieure, 45 rue d'Ulm, 75230 Paris, France

J. Chem. Inf. Comput. Sci., 2001, 41 (2), pp 376–386

DOI: 10.1021/ci000129s

Publication Date (Web): January 27, 2001

†

University of Exeter.

Corresponding author fax: 44 1392 263 434; e-mail: P.W.Fowler@ex.ac.uk.

‡

Ecole Normale Supérieure.

Abstract

The notion of d-code is extended to general polyhedra by defining maximum sets of vertices with pairwise separation ≥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.

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