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A236557 Vertex solid angle (steradians) in a regular icosahedron. 4

%I #15 May 22 2023 02:45:30

%S 2,6,3,4,5,4,7,0,2,6,0,4,4,7,5,4,6,5,9,6,5,1,3,0,3,4,6,7,4,9,2,4,0,2,

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

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

%N Vertex solid angle (steradians) in a regular icosahedron.

%H Stanislav Sykora, <a href="/A236557/b236557.txt">Table of n, a(n) for n = 1..2000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Platonic_solid">Platonic solid</a>.

%F Equals 2*Pi - 5*arcsin(2/3).

%e 2.6345470260447546596513034674924022914118092285116431884051417273...

%t RealDigits[2*Pi - 5*ArcSin[2/3], 10, 120][[1]] (* _Amiram Eldar_, May 22 2023 *)

%o (PARI) 2*Pi-5*asin(2/3)

%Y Cf. Analogs: A236555 (tetrahedron), A236556 (octahedron), A019669 (cube), A236558 (dodecahedron).

%K nonn,cons,easy

%O 1,1

%A _Stanislav Sykora_, Jan 28 2014

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