Skip to main content
MathOverflow

You are not logged in. Your edit will be placed in a queue until it is peer reviewed.

We welcome edits that make the post easier to understand and more valuable for readers. Because community members review edits, please try to make the post substantially better than how you found it, for example, by fixing grammar or adding additional resources and hyperlinks.

10
  • 4
    $\begingroup$ Wait, the dodecahedron is not a minimum energy configuration? $\endgroup$
    – M. Winter
    Commented Feb 6, 2021 at 2:50
  • 6
    $\begingroup$ @M.Winter Surprisingly, it seems that the minimal energy for 20 points is not related to the dodecahedron. Nor are the vertices of the cube the optimal arrangement for 8 points. A 2003 survey article by Atiyah & Sutcliffe includes citations and nice illustrations of the polyhedra (arxiv.org/abs/math-ph/0303071). $\endgroup$
    – Brian Hopkins
    Commented Feb 6, 2021 at 5:50
  • 2
    $\begingroup$ @M.Winter I find it disappointingly unasthetic too! I can't help feeling that, if we can't even get a pentagon on a dodecahedron, then surely they can't show up anywhere else. Dodecahedra are the only places that pentagons belong! :) $\endgroup$
    – Alex Meiburg
    Commented Feb 6, 2021 at 7:29
  • 2
    $\begingroup$ @BrianHopkins. Did you notice the following sentence of the introduction ? A particularly interesting application of polyhedra in biology is provided by the structure of spherical shells, such as HIV which is built around a trivalent polyhedron with icosahedral symmetry. A few years later, the authors would have changed HIV into Coronavirus. $\endgroup$
    – Denis Serre
    Commented Feb 6, 2021 at 10:09
  • 1
    $\begingroup$ I guess a related conjecture: among all the optimal solutions to Thomson's problem, only a finite number of them have squares. The same idea that, eventually, everything becomes triangle packings. $\endgroup$
    – Alex Meiburg
    Commented Feb 8, 2021 at 0:32