%I #28 Aug 14 2023 10:32:31
%S 7,5,5,7,6,1,3,1,4,0,7,6,1,7,0,7,3,0,4,8,0,1,3,3,7,0,2,0,2,5,0,0,1,3,
%T 9,2,6,3,8,4,4,4,7,8,8,8,9,3,5,6,1,0,5,9,2,2,9,5,8,2,8,9,2,0,3,9,1,0,
%U 6,8,4,5,2,2,1,9,4,8,2,6,2,0,6,3,5,6,0,4,9,4,7,6,0,8,6,8,2,7,0,4,1,1,9,3,1
%N Decimal expansion of radius of inscribed sphere about a regular icosahedron with edge = 1.
%C Icosahedron: A three-dimensional figure with 20 equilateral triangle faces, 12 vertices, and 30 edges.
%H Ivan Panchenko, <a href="/A179294/b179294.txt">Table of n, a(n) for n = 0..1000</a>
%H Dr. Math, <a href="http://mathforum.org/dr.math/faq/formulas/faq.polyhedron.html#icosahedron">Icosahedron</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Icosahedron">Icosahedron</a>
%H MathWorld, <a href="http://mathworld.wolfram.com/Icosahedron.html">Icosahedron</a>
%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>
%F Sqrt(42 + 18*sqrt(5))/12.
%e 0.75576131407617073048013370202500139263844478889356105922958289203910...
%t a=1;RealDigits[N[(Sqrt[42+18Sqrt[5]]/12)*a,175]]
%Y Cf. A010527, A102208, A179290, A179292.
%Y Cf. Platonic solids inradii: A020781 (tetrahedron), A020763 (octahedron), A237603 (dodecahedron).
%K nonn,cons,easy
%O 0,1
%A _Vladimir Joseph Stephan Orlovsky_, Jul 09 2010
%E Partially rewritten by _Charles R Greathouse IV_, Feb 03 2011
|