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A374755
Decimal expansion of the surface area of a regular dodecahedron having unit inradius.
5
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, 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, 5, 1, 0, 1, 2, 1, 9, 9, 9, 7, 3, 5, 7, 0, 9, 4, 4, 8, 8, 1, 6, 6
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
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.
FORMULA
Equals 30*sqrt(130 - 58*sqrt(5)).
Equals 60*sqrt(3 - A001622)/A098317.
Equals 4*Pi/A374772.
Equals 3*A374753.
EXAMPLE
16.6508730855465308072112963409855177222127946386...
MATHEMATICA
First[RealDigits[30*Sqrt[130 - 58*Sqrt[5]], 10, 100]]
CROSSREFS
Cf. A374753 (dodecahedral conjecture), A374772, A374837, A374838.
Sequence in context: A019126 A019206 A104225 * A292179 A255823 A011188
KEYWORD
nonn,cons
AUTHOR
Paolo Xausa, Jul 20 2024
STATUS
approved