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A179292 Decimal expansion of radius of inscribed sphere of an icosahedron with radius of circumscribed sphere = 1.

%I A179292 #12 Feb 16 2025 08:33:12
%S A179292 7,9,4,6,5,4,4,7,2,2,9,1,7,6,6,1,2,2,9,5,5,5,3,0,9,2,8,3,2,7,5,9,4,0,
%T A179292 4,2,0,2,6,5,9,0,5,8,8,3,0,9,2,6,4,8,0,1,7,5,4,9,5,5,7,7,5,0,0,8,4,3,
%U A179292 8,6,4,4,9,7,1,7,3,7,1,1,6,7,9,3,0,2,7,2,9,9,4,8,4,8,7,0,8,7,1,3,7,8,5,2,8
%N A179292 Decimal expansion of radius of inscribed sphere of an icosahedron with radius of circumscribed sphere = 1.
%C A179292 Icosahedron: A three-dimensional figure with 20 equilateral triangle faces, 12 vertices, and 30 edges.
%H A179292 Mathforum, <a href="http://mathforum.org/dr.math/faq/formulas/faq.polyhedron.html#icosahedron">Icosahedron</a>
%H A179292 Wikipedia, <a href="http://en.wikipedia.org/wiki/Icosahedron">Icosahedron</a>
%H A179292 MathWorld, <a href="https://mathworld.wolfram.com/Icosahedron.html">Icosahedron</a>
%H A179292 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.
%F A179292 Sqrt(75 + 30*sqrt(5))/15.
%e A179292 0.794654472291766122955530928327594042026590588309264801754955775008438...
%t A179292 R=1;RealDigits[N[(Sqrt[75+30*Sqrt[5]]/15)*R,175]]
%o A179292 (PARI) polrootsreal(45*x^4-30*x^2+1)[4] \\ _Charles R Greathouse IV_, Sep 02 2024
%o A179292 (PARI) sqrt(6/sqrt(5)+3)/3 \\ _Charles R Greathouse IV_, Sep 02 2024
%Y A179292 Cf. A010527, A102208, A179290.
%K A179292 nonn,cons,easy
%O A179292 0,1
%A A179292 _Vladimir Joseph Stephan Orlovsky_, Jul 09 2010
%E A179292 Offset corrected, keyword:cons added by _R. J. Mathar_, Jul 11 2010