Fullerenes and coordination polyhedra versus half-cube embeddings

摘要: A fullerene Fn is a 3-regular (or cubic) polyhedral carbon molecule for which the n vertices - carbons atoms are arranged in 12 pentagons and (n/2 10) hexagons. Only finite number of fullerenes expected to be, up scale, isometrically embeddable into hypercube. Looking list such fullerenes, we first check embeddability all < 60 preferable Cn 86 their duals. Then, consider some infinite families, including with icosahedral symmetry, describe virus capsids, onion-like metallic clusters geodesic domes. Quasi-embeddings analogues considered. We also present results on chemically relevant polyhedra as coordination cluster polyhedra. Finally conjecture that known complete its relevance Katsura model vesicles cells.