cp's OEIS Frontend

A374755 Decimal expansion of the surface area of a regular dodecahedron having unit inradius.

%I A374755 #25 Sep 03 2025 09:14:03
%S A374755 1,6,6,5,0,8,7,3,0,8,5,5,4,6,5,3,0,8,0,7,2,1,1,2,9,6,3,4,0,9,8,5,5,1,
%T A374755 7,7,2,2,2,1,2,7,9,4,6,3,8,6,4,7,4,9,6,6,0,1,3,3,5,2,6,1,5,9,0,6,1,6,
%U A374755 5,1,0,1,2,1,9,9,9,7,3,5,7,0,9,4,4,8,8,1,6,6
%N A374755 Decimal expansion of the surface area of a regular dodecahedron having unit inradius.
%C A374755 Bezdek's strong dodecahedral conjecture (proved by Hales, see links) states that, in any packing of unit spheres in the Euclidean 3-space, the surface area of every bounded Voronoi cell is at least this value.
%H A374755 Paolo Xausa, <a href="/A374755/b374755.txt">Table of n, a(n) for n = 2..10000</a>
%H A374755 Károly Bezdek, <a href="https://doi.org/10.1515/crll.2000.001">On a stronger form of Rogers' lemma and the minimum surface area of Voronoi cells in unit ball packings</a>, Journal für die reine und angewandte Mathematik, No. 518, 2000, pp. 131-143.
%H A374755 Thomas C. Hales, <a href="https://doi.org/10.48550/arXiv.1110.0402">The Strong Dodecahedral Conjecture and Fejes Toth's Conjecture on Sphere Packings with Kissing Number Twelve</a>, arXiv:1110.0402 [math.MG], 2012.
%H A374755 Wikipedia, <a href="https://en.wikipedia.org/wiki/Regular_dodecahedron">Regular dodecahedron</a>.
%F A374755 Equals 30*sqrt(130 - 58*sqrt(5)).
%F A374755 Equals 60*sqrt(3 - A001622)/A098317.
%F A374755 Equals 4*Pi/A374772.
%F A374755 Equals 3*A374753.
%F A374755 Minimal polynomial: x^4 - 234000*x^2 + 64800000. - _Stefano Spezia_, Sep 03 2025
%e A374755 16.6508730855465308072112963409855177222127946386...
%t A374755 First[RealDigits[30*Sqrt[130 - 58*Sqrt[5]], 10, 100]]
%Y A374755 Cf. A374753 (dodecahedral conjecture), A374772, A374837, A374838.
%Y A374755 Cf. A001622, A098317, A131595.
%K A374755 nonn,cons,changed
%O A374755 2,2
%A A374755 _Paolo Xausa_, Jul 20 2024