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

%I A236555 #20 Mar 11 2025 11:42:50
%S A236555 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,
%T A236555 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,
%U A236555 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
%N A236555 Decimal expansion of the steradian solid angle subtended by one triangular facet of the cuboctahedron.
%C A236555 Also the vertex solid angle of a regular tetrahedron.
%H A236555 Stanislav Sykora, <a href="/A236555/b236555.txt">Table of n, a(n) for n = 0..2000</a>
%H A236555 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Cuboctahedron.html">Cuboctahedron</a>
%H A236555 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SphericalPolygon.html">Spherical Polygon</a>
%H A236555 Wikipedia, <a href="http://en.wikipedia.org/wiki/Platonic_solid">Platonic solid</a>
%H A236555 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A236555 arccos(23/27).
%F A236555 3*arcsin(2*sqrt(2)/3) - Pi. - _Bradley Klee_, Oct 04 2018
%F A236555 8*A236555 + 6*A236556 = 4*Pi. - _Bradley Klee_, Oct 04 2018
%F A236555 Equals 2*arctan(sqrt(2)/5). - _R. J. Mathar_, Mar 11 2025
%e A236555 0.55128559843253080794214415146445924293385062869017869619170040868416...
%t A236555 RealDigits[N[ArcCos[23/27], 107]][[1]] (* _T. D. Noe_, Jan 29 2014 *)
%o A236555 (PARI) acos(23/27) \\ _Charles R Greathouse IV_, Feb 10 2025
%Y A236555 Cf. A236556. Icosidodecahedron: A319881, A319883. Vertex Angles: A019669, A236557, A236558.
%K A236555 nonn,cons,easy
%O A236555 0,1
%A A236555 _Stanislav Sykora_, Jan 28 2014
%E A236555 Definition corrected by _Bradley Klee_, Oct 04 2018