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
Joel D. Berman and Kitt Hanes, Volumes of Polyhedra Inscribed in the Unit Sphere in E3. Mathematische Annalen 188, 78-84 (1970).
Donald W. Grace, Search For Largest Polyhedra, Mathematics of Computation 17 (1963), pp. 197-199.
Matt Parker, The search for the biggest shape in the universe, YouTube video, 2024.
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
KEYWORD
nonn,cons
AUTHOR
Hugo Pfoertner, Nov 29 2020
STATUS
approved