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A339261
Decimal expansion of the conjecturally maximum possible volume of a polyhedron with 9 vertices inscribed in the unit sphere.
4
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
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
KEYWORD
nonn,cons
AUTHOR
Hugo Pfoertner, Dec 05 2020
STATUS
approved