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A339262
Decimal expansion of the conjecturally maximum possible volume of a polyhedron with 10 vertices inscribed in the unit sphere.
4
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, 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, 0, 8, 1, 2, 7, 9, 9, 0, 9, 1, 8, 1, 4, 8, 8, 4, 6, 3, 3
OFFSET
1,1
COMMENTS
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.
LINKS
R. H. Hardin, N. J. A. Sloane and W. D. Smith, Maximal Volume Spherical Codes.
Hugo Pfoertner, Visualization of Polyhedron, (1999).
EXAMPLE
2.218711131545399403247282751128417013810725374663344381750049084201...
CROSSREFS
Cf. A010527 (volume of double 5-pyramid), A081314, A081366, A122553 (volume of octahedron), A339259, A339260, A339261, A339263.
Sequence in context: A096440 A181738 A121350 * A198569 A135080 A348724
KEYWORD
nonn,cons
AUTHOR
Hugo Pfoertner, Dec 07 2020
STATUS
approved