A339261 Decimal expansion of the conjecturally maximum possible volume of a polyhedron with 9 vertices inscribed in the unit sphere.

2, 0, 4, 3, 7, 5, 0, 1, 1, 5, 8, 9, 9, 6, 3, 9, 8, 4, 1, 1, 6, 6, 3, 6, 5, 4, 6, 4, 2, 2, 6, 9, 8, 5, 3, 3, 3, 8, 6, 3, 2, 6, 0, 6, 1, 5, 2, 9, 4, 7, 5, 1, 8, 1, 8, 7, 1, 8, 2, 1, 5, 7, 9, 5, 6, 8, 7, 1, 0, 4, 2, 6, 4, 0, 9, 2, 7, 7, 1, 4, 0, 6, 1, 7, 8, 5, 9

Offset

1,1

Links

Table of n, a(n) for n=1..87.

R. H. Hardin, N. J. A. Sloane and W. D. Smith, Maximal Volume Spherical Codes.

Hugo Pfoertner, Visualization of Polyhedron, (1999).

Hugo Pfoertner, 9-Vertex-Polyhedron with maximum volume inscribed in a sphere, YouTube video, Feb 10 2021.

Formula

Equals 3*sqrt(2*sqrt(3) - 3).

Example

2.0437501158996398411663654642269853338632606152947518187182157956871...

Mathematica

RealDigits[3*Sqrt[2*Sqrt[3] - 3], 10, 120][[1]] (* Amiram Eldar, Jun 28 2023 *)

Prog

(PARI) 3*sqrt(2*sqrt(3) - 3)

Crossrefs

Cf. A010527 (volume of double 5-pyramid), A081314, A081366, A122553 (volume of octahedron), A339259, A339260, A339261, A339262, A339263.

Sequence in context: A291937 A243488 A154849 * A345232 A277333 A248663

Adjacent sequences: A339258 A339259 A339260 * A339262 A339263 A339264

Keyword

nonn,cons

Author

Hugo Pfoertner, Dec 05 2020

Status

approved