A339262 Decimal expansion of the conjecturally maximum possible volume of a polyhedron with 10 vertices inscribed in the unit sphere.

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

Author

Hugo Pfoertner, Dec 07 2020

Keywords

• nonn
• cons

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.

Examples

			2.218711131545399403247282751128417013810725374663344381750049084201...
		

Links

• R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Maximal Volume Spherical Codes.
• Hugo Pfoertner, Visualization of Polyhedron, (1999).
• Hugo Pfoertner, Number of edges incident with the 10 vertices, video (2021).

Crossrefs

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