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%I #26 Aug 21 2023 11:46:13
%S 5,1,4,8,3,4,8,5,5,6,1,9,9,5,1,5,6,4,6,3,3,0,8,1,2,9,4,6,1,1,6,0,1,9,
%T 0,6,4,1,0,0,8,6,4,1,1,6,3,8,6,7,2,4,1,4,8,4,5,0,7,1,3,6,7,5,3,9,8,0,
%U 3,2,4,7,9,0,5,0,8,5,7,7,1,3,0,2,9,8,3,7,3,2,5,6,2,9,9,4,3,1,0,9,6,7,4,0,0
%N Decimal expansion of the surface index of a regular icosahedron.
%C Equivalently, surface area of a regular icosahedron with unit volume. Among Platonic solids, surface indices decrease with increasing number of faces: A232812 (tetrahedron), 6.0 (cube = hexahedron), A232811 (octahedron), A232810 (dodecahedron), and this one.
%C An algebraic integer of degree 12 with minimal polynomial x^12 - 41115600x^6 + 765275040000. - _Charles R Greathouse IV_, Apr 25 2016
%H Stanislav Sykora, <a href="/A232809/b232809.txt">Table of n, a(n) for n = 1..1000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Platonic_solid">Platonic solid</a>.
%H <a href="/index/Al#algebraic_12">Index entries for algebraic numbers, degree 12</a>
%F Equals 5*sqrt(3)/(5*(3+sqrt(5))/12)^(2/3).
%F Equals 10*A010527/A102208^(2/3).
%e 5.14834855619951564633081294611601906410086411638672414845...
%t RealDigits[5*Sqrt[3]/(5*(3+Sqrt[5])/12)^(2/3), 10, 120][[1]] (* _Amiram Eldar_, May 25 2023 *)
%o (PARI) 5*sqrt(3)/(5*(3+sqrt(5))/12)^(2/3) \\ _Charles R Greathouse IV_, Apr 25 2016
%Y Cf. A010527, A102208 (solid index of a sphere), A232808, A232810, A232811, A232812.
%K nonn,cons,easy
%O 1,1
%A _Stanislav Sykora_, Dec 01 2013
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