A236556 Decimal expansion of the steradian solid angle subtended by one square facet of the cuboctahedron.

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

Offset: 1

Author

Stanislav Sykora, Jan 28 2014

Keywords

• nonn
• cons
• easy

Comments

Also the vertex solid angle of a regular octahedron.

Examples

			1.35934763781648774838557005356705626555297876132983228572769584995966...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..2000
• Eric Weisstein's World of Mathematics, Cuboctahedron.
• Eric Weisstein's World of Mathematics, Spherical Polygon.
• Wikipedia, Platonic solid.
• Index entries for transcendental numbers.

Crossrefs

Cf. A188615, A236555. Icosidodecahedron: A319881, A319883. Vertex Angles: A019669, A236557, A236558.

Programs

Maple

evalf(4*arcsin(1/3),100) ; # R. J. Mathar, Apr 26 2021

Mathematica

RealDigits[4*ArcSin[1/3], 10, 120][[1]] (* Amiram Eldar, May 22 2023 *)

PARI

4*asin(1/3)

Formula

Equals 4*arcsin(1/3) = 4*A188615.

Equals 2*Pi - 4*arcsin(2*sqrt(2)/3). - Bradley Klee, Oct 04 2018

8*A236555 + 6*this = 4*Pi. - Bradley Klee, Oct 04 2018

Extensions

Definition corrected by Bradley Klee, Oct 04 2018