A339260 Decimal expansion of the maximum possible volume of a polyhedron with 8 vertices inscribed in the unit sphere.

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

Offset

1,2

Comments

Berman and Hanes (see link, page 81) proved in 1970 that an arrangement of 8 points on the surface of a sphere with 4 points with node degree 4 and 4 points with node degree 5 is the one with a maximum volume of their convex hull.

Links

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

Joel D. Berman and Kitt Hanes, Volumes of Polyhedra Inscribed in the Unit Sphere in E3. Mathematische Annalen 188, 78-84 (1970).

Hugo Pfoertner, Visualization of Polyhedron, (1999).

Formula

Equals sqrt((475 + 29*sqrt(145))/250).

Example

1.8157161042244203975084949306331777890131009552754398376663729...

Mathematica

RealDigits[Sqrt[(475 + 29*Sqrt[145])/250], 10, 120][[1]] (* Amiram Eldar, Jun 01 2023 *)

Prog

(PARI) sqrt((475+29*sqrt(145))/250)

Crossrefs

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

Sequence in context: A126585 A157289 A194097 * A226604 A154213 A353920

Adjacent sequences: A339257 A339258 A339259 * A339261 A339262 A339263

Keyword

nonn,cons

Author

Hugo Pfoertner, Nov 29 2020

Status

approved