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• W2051640593 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 ≤ 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 ≤ 60 vertices) with adjacent pentagons, only 15; the soccer ball ( n = 60); and among the 216,739 large cages with 60 < n ≤ 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." @default.
• W2051640593 created "2016-06-24" @default.
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• W2051640593 date "2008-12-09" @default.
• W2051640593 modified "2023-09-27" @default.
• W2051640593 title "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" @default.
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• W2051640593 doi "https://doi.org/10.1073/pnas.0807603105" @default.
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