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

Author

Hugo Pfoertner, Dec 05 2020

Keywords

• nonn
• cons

Examples

			2.0437501158996398411663654642269853338632606152947518187182157956871...
		

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.

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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