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Decimal expansion of the conjecturally maximum possible volume of a polyhedron with 9 vertices inscribed in the unit sphere.
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%I #13 Jun 28 2023 08:21:33

%S 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,

%T 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,

%U 0,4,2,6,4,0,9,2,7,7,1,4,0,6,1,7,8,5,9

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

%H R. H. Hardin, N. J. A. Sloane and W. D. Smith, <a href="http://neilsloane.com/maxvolumes">Maximal Volume Spherical Codes</a>.

%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sphere/volmax/pages/09.htm">Visualization of Polyhedron</a>, (1999).

%H Hugo Pfoertner, <a href="https://www.youtube.com/watch?v=vyWvE6lPIt8">9-Vertex-Polyhedron with maximum volume inscribed in a sphere</a>, YouTube video, Feb 10 2021.

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

%e 2.0437501158996398411663654642269853338632606152947518187182157956871...

%t RealDigits[3*Sqrt[2*Sqrt[3] - 3], 10, 120][[1]] (* _Amiram Eldar_, Jun 28 2023 *)

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

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

%K nonn,cons

%O 1,1

%A _Hugo Pfoertner_, Dec 05 2020