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%I #8 Dec 15 2024 07:24:47
%S 1,3,7,4,5,1,7,4,4,7,0,1,0,4,7,1,6,4,7,2,7,5,1,0,0,0,0,6,3,9,7,4,2,3,
%T 6,7,4,4,8,1,0,2,7,3,3,3,0,7,0,7,5,3,0,7,8,6,1,7,6,6,9,8,6,5,8,9,8,8,
%U 8,6,8,7,0,8,2,0,9,0,5,9,4,2,0,8,8,9,3,7,4,4
%N Decimal expansion of the inradius of a triakis icosahedron with unit shorter edge length.
%C The triakis icosahedron is the dual polyhedron of the truncated dodecahedron.
%H Paolo Xausa, <a href="/A378975/b378975.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriakisIcosahedron.html">Triakis Icosahedron</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Triakis_icosahedron">Triakis icosahedron</a>.
%F Equals sqrt((477 + 199*sqrt(5))/488) = sqrt((477 + 199*A002163)/488).
%e 1.37451744701047164727510000639742367448102733307...
%t First[RealDigits[Sqrt[(477 + 199*Sqrt[5])/488], 10, 100]] (* or *)
%t First[RealDigits[PolyhedronData["TriakisIcosahedron", "Inradius"], 10, 100]]
%Y Cf. A378973 (surface area), A378974 (volume), A378976 (midradius), A378977 (dihedral angle).
%Y Cf. A002163.
%K nonn,cons,easy,new
%O 1,2
%A _Paolo Xausa_, Dec 14 2024