Geodesic
Enumeration of irreducible contact graphs on the sphere
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 2, pp. 125-145

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In this article, using the computer, are enumerated all locally-rigid packings by $N$ congruent circles (spherical caps) on the unit sphere $\mathbb S^2$ with $N12$. This is equivalent to the enumeration of irreducible spherical contact graphs. 
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     author = {O. R. Musin and A. S. Tarasov},
     title = {Enumeration of irreducible contact graphs on the sphere},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2013_18_2_a9/}
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O. R. Musin; A. S. Tarasov. Enumeration of irreducible contact graphs on the sphere. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 2, pp. 125-145. http://geodesic.mathdoc.fr/item/FPM_2013_18_2_a9/