A374753 Decimal expansion of the volume of a regular dodecahedron having unit inradius.

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, 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, 3, 6, 7, 0, 7, 3, 3, 3, 2, 4, 5, 2, 3, 6, 4, 8, 2, 9, 3, 8, 8, 9

Offset: 1

Author

Paolo Xausa, Jul 19 2024

Keywords

• nonn
• cons

Comments

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.

Examples

			5.55029102851551026907043211366183924073759821288...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Thomas C. Hales and Sean McLaughlin, A proof of the dodecahedral conjecture, arXiv:math/9811079 [math.MG], 2008.
• Thomas C. Hales and Sean McLaughlin, The Dodecaheral Conjecture, Journal of the American Mathematical Society, Vol. 23, No. 2, April 2010, pp. 299-344.
• Wikipedia, Dodecahedral conjecture.
• Wikipedia, Regular dodecahedron.
• Index entries for algebraic numbers, degree 4.

Crossrefs

Cf. A019699, A374755 (strong dodecahedral conjecture), A374772 (density).

Programs

Mathematica

First[RealDigits[10*Sqrt[130 - 58*Sqrt[5]], 10, 100]]

Formula

Equals (4/3)*Pi/A374772 = 10*A019699/A374772.

Equals 10*sqrt(130 - 58*sqrt(5)).

Equals A374755/3.