Packing of equal regular pentagons on a sphere
Tibor Tarnai, Zsolt Gáspár · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2001
How must n equal non–overlapping regular spherical pentagons be packed on a sphere so that the angular radius of the circumcircles of the pentagons will be as great as possible? In this paper, locally extremal results as conjectured solutions of this problem for n = 1, 2, 3, 4, 7, 9, 11, 12 are given and locally non–extremal results for n 7equals; 10 and 32 are presented. The local optima are obtained by using a mechanical method similar to the ‘heating technique7rsquo; developed for spherical circle packings. Locally extremal configurations under octahedral and icosahedral symmetry constraints are also shown for n = 24 and 72. A table is given of the known best arrangements and of the newly discovered best arrangements.