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%I #23 Jul 23 2024 06:44:54
%S 5,5,5,0,2,9,1,0,2,8,5,1,5,5,1,0,2,6,9,0,7,0,4,3,2,1,1,3,6,6,1,8,3,9,
%T 2,4,0,7,3,7,5,9,8,2,1,2,8,8,2,4,9,8,8,6,7,1,1,1,7,5,3,8,6,3,5,3,8,8,
%U 3,6,7,0,7,3,3,3,2,4,5,2,3,6,4,8,2,9,3,8,8,9
%N Decimal expansion of the volume of a regular dodecahedron having unit inradius.
%C The dodecahedral conjecture (proved in 1988 by Thomas C. Hales and Sean McLaughlin, see links) states that, in any packing of unit spheres in the Euclidean 3-space, every Voronoi cell has volume at least equal to this value.
%H Paolo Xausa, <a href="/A374753/b374753.txt">Table of n, a(n) for n = 1..10000</a>
%H Thomas C. Hales and Sean McLaughlin, <a href="https://doi.org/10.48550/arXiv.math/9811079">A proof of the dodecahedral conjecture</a>, arXiv:math/9811079 [math.MG], 2008.
%H Thomas C. Hales and Sean McLaughlin, <a href="https://doi.org/10.1090/S0894-0347-09-00647-X">The Dodecaheral Conjecture</a>, Journal of the American Mathematical Society, Vol. 23, No. 2, April 2010, pp. 299-344.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Dodecahedral_conjecture">Dodecahedral conjecture</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Regular_dodecahedron">Regular dodecahedron</a>.
%F Equals (4/3)*Pi/A374772 = 10*A019699/A374772.
%F Equals 10*sqrt(130 - 58*sqrt(5)).
%F Equals A374755/3.
%e 5.55029102851551026907043211366183924073759821288...
%t First[RealDigits[10*Sqrt[130 - 58*Sqrt[5]], 10, 100]]
%Y Cf. A019699, A374755 (strong dodecahedral conjecture), A374772 (density).
%K nonn,cons
%O 1,1
%A _Paolo Xausa_, Jul 19 2024