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

0,1

Comments

Also the vertex solid angle of a regular tetrahedron.

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.

Formula

Equals arccos(23/27).

Equals 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

Equals 3*arccos(1/3) - Pi = 3*A137914 - Pi. - Robert FERREOL, Jan 16 2026

Example

0.55128559843253080794214415146445924293385062869017869619170040868416...

Mathematica

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

Prog

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

Crossrefs

Cf. A236556. Icosidodecahedron: A319881, A319883. Vertex Angles: A019669, A236557, A236558.

Sequence in context: A232651 A390073 A145227 * A282969 A046095 A322545

Adjacent sequences: A236552 A236553 A236554 * A236556 A236557 A236558

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Jan 28 2014

Extensions

Definition corrected by Bradley Klee, Oct 04 2018

Status

approved