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    $\begingroup$ Are you interested in having an understandable algorithm to generate these graphs? Would you be happy with routine that imports the graphs generated by the program described here? $\endgroup$ Commented Nov 6, 2017 at 2:04
  • $\begingroup$ Wow, what a find! In an ideal world I'd have the whole functionality of Buckygen in Mathematica! But as that's obviously a huge task whose benefits I wouldn't reap for a very long time, I would gladly settle for just the icosahedral ones (those where the pentagons are evenly distributed). $\endgroup$ Commented Nov 6, 2017 at 6:23
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    $\begingroup$ That's a neat paper, @Jason! If you can find time to show how to use it with Mathematica, it can be interesting. $\endgroup$ Commented Nov 6, 2017 at 6:33
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    $\begingroup$ BTW, I presume you're aware of Goldberg polyhedra? $\endgroup$ Commented Nov 11, 2017 at 3:34
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    $\begingroup$ In fact, the paper I'm following above gives a nice visual explanation of Goldberg's original construction, and I called my variables Gi and Gj for Goldberg :) $\endgroup$ Commented Nov 11, 2017 at 9:12