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

1,2

Comments

Also the vertex solid angle of a regular octahedron.

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.

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

Example

1.35934763781648774838557005356705626555297876132983228572769584995966...

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 *)

Prog

(PARI) 4*asin(1/3)

Crossrefs

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

Sequence in context: A303772 A200510 A138055 * A189044 A299793 A356527

Adjacent sequences: A236553 A236554 A236555 * A236557 A236558 A236559

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Jan 28 2014

Extensions

Definition corrected by Bradley Klee, Oct 04 2018

Status

approved