OFFSET
2,2
COMMENTS
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.
LINKS
Paolo Xausa, Table of n, a(n) for n = 2..10000
Károly Bezdek, On a stronger form of Rogers' lemma and the minimum surface area of Voronoi cells in unit ball packings, Journal für die reine und angewandte Mathematik, No. 518, 2000, pp. 131-143.
Thomas C. Hales, The Strong Dodecahedral Conjecture and Fejes Toth's Conjecture on Sphere Packings with Kissing Number Twelve, arXiv:1110.0402 [math.MG], 2012.
Wikipedia, Regular dodecahedron.
FORMULA
EXAMPLE
16.6508730855465308072112963409855177222127946386...
MATHEMATICA
First[RealDigits[30*Sqrt[130 - 58*Sqrt[5]], 10, 100]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Paolo Xausa, Jul 20 2024
STATUS
approved