%I #7 Dec 08 2020 02:33:24

%S 2,2,1,8,7,1,1,1,3,1,5,4,5,3,9,9,4,0,3,2,4,7,2,8,2,7,5,1,1,2,8,4,1,7,

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

%U 0,8,1,2,7,9,9,0,9,1,8,1,4,8,8,4,6,3,3

%N Decimal expansion of the conjecturally maximum possible volume of a polyhedron with 10 vertices inscribed in the unit sphere.

%C The polyhedron (see linked illustration) has vertices at the poles and two square rings of vertices rotated by Pi/4 against each other, with a polar angle of approx. +-62.89908285 degrees against the poles. The polyhedron is completely described by this angle and its order 16 symmetry. It would be desirable to know a closed formula representation of this angle and the volume.

%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/10.htm">Visualization of Polyhedron</a>, (1999).

%e 2.218711131545399403247282751128417013810725374663344381750049084201...

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

%K nonn,cons

%O 1,1

%A _Hugo Pfoertner_, Dec 07 2020