A236555 Decimal expansion of the steradian solid angle subtended by one triangular facet of the cuboctahedron.

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

Offset: 0

Author

Stanislav Sykora, Jan 28 2014

Keywords

• nonn
• cons
• easy

Comments

Also the vertex solid angle of a regular tetrahedron.

Examples

			0.55128559843253080794214415146445924293385062869017869619170040868416...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 0..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. A236556. Icosidodecahedron: A319881, A319883. Vertex Angles: A019669, A236557, A236558.

Programs

Mathematica

RealDigits[N[ArcCos[23/27], 107]][[1]] (* T. D. Noe, Jan 29 2014 *)

PARI

acos(23/27) \\ Charles R Greathouse IV, Feb 10 2025

Formula

arccos(23/27).

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

8*A236555 + 6*A236556 = 4*Pi. - Bradley Klee, Oct 04 2018

Equals 2*arctan(sqrt(2)/5). - R. J. Mathar, Mar 11 2025

Extensions

Definition corrected by Bradley Klee, Oct 04 2018