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

1,1

Comments

The dodecahedral conjecture (proved in 1998 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.

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], 1998-2008.

Thomas C. Hales and Sean McLaughlin, The Dodecaheral Conjecture, Journal of the American Mathematical Society, Vol. 23, No. 2 (April 2010), pp. 299-344.

Polytope Wiki, Dodecahedron.

Eric Weisstein's World of Mathematics, Regular Dodecahedron.

Wikipedia, Dodecahedral conjecture.

Wikipedia, Regular dodecahedron.

Index entries for algebraic numbers, degree 4.

Formula

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

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

Equals A374755/3.

Minimal polynomial: x^4 - 26000*x^2 + 800000. - Amiram Eldar, May 18 2026

Example

5.55029102851551026907043211366183924073759821288...

Mathematica

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

Crossrefs

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

Sequence in context: A344235 A019253 A019173 * A230192 A172359 A379377

Adjacent sequences: A374750 A374751 A374752 * A374754 A374755 A374756

Keyword

nonn,cons

Author

Paolo Xausa, Jul 19 2024

Status

approved