ArticleProceedings of the National Academy of Sciences of the United States of America2008
A geometric constraint, the head-to-tail exclusion rule, may be the basis for the isolated-pentagon rule in fullerenes with more than 60 vertices.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2008. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- The Interplay of Curvature, Geometry, and Topology Shapes Tissue Organisation in Epithelial Shells.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2026Article
- Fourth class of convex equilateral polyhedron with polyhedral symmetry related to fullerenes and viruses.Proceedings of the National Academy of Sciences of the United States of America · 2014Article
- The stabilization of fused-pentagon fullerene molecules.Nature chemistry · 2009Review
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2 authors.
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Abstract
Carbon atoms self-assemble into the famous soccer-ball shaped Buckminsterfullerene (C(60)), the smallest fullerene cage that obeys the isolated-pentagon rule (IPR). Carbon atoms self-assemble into larger (n > 60 vertices) empty cages as well-but only the few that obey the IPR-and at least 1 small fullerene (n <or= 60) with adjacent pentagons. Clathrin protein also self-assembles into small fullerene cages with adjacent pentagons, but just a few of those. We asked why carbon atoms and clathrin proteins self-assembled into just those IPR and small cage isomers. In answer, we described a geometric constraint-the head-to-tail exclusion rule-that permits self-assembly of just the following fullerene cages: among the 5,769 possible small cages (n <or= 60 vertices) with adjacent pentagons, only 15; the soccer ball (n = 60); and among the 216,739 large cages with 60 < n <or= 84 vertices, only the 50 IPR ones. The last finding was a complete surprise. Here, by showing that the largest permitted fullerene with adjacent pentagons is one with 60 vertices and a ring of interleaved hexagons and pentagon pairs, we prove that for all n > 60, the head-to-tail exclusion rule permits only (and all) fullerene cages and nanotubes that obey the IPR. We therefore suggest that self-assembly that obeys the IPR may be explained by the head-to-tail exclusion rule, a geometric constraint.
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