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A379134 Decimal expansion of the inradius of a pentakis dodecahedron with unit shorter edge length.

%I A379134 #9 Feb 05 2025 10:28:29
%S A379134 1,4,4,5,3,3,1,9,2,5,6,5,2,2,1,4,8,2,8,3,1,5,8,5,1,2,4,9,1,0,2,0,8,1,
%T A379134 1,9,7,7,2,3,8,7,1,1,7,7,8,4,3,0,3,8,9,7,1,6,2,5,7,9,0,6,7,3,8,1,7,3,
%U A379134 5,4,5,5,1,5,9,4,0,1,5,6,3,8,4,2,8,0,6,3,3,2
%N A379134 Decimal expansion of the inradius of a pentakis dodecahedron with unit shorter edge length.
%C A379134 The pentakis dodecahedron is the dual polyhedron of the truncated icosahedron.
%H A379134 Paolo Xausa, <a href="/A379134/b379134.txt">Table of n, a(n) for n = 1..10000</a>
%H A379134 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentakisDodecahedron.html">Pentakis Dodecahedron</a>.
%H A379134 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentakis_dodecahedron">Pentakis dodecahedron</a>.
%H A379134 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.
%F A379134 Equals sqrt(477/436 + 97*sqrt(5)/218) = sqrt(477/436 + 97*A002163/218).
%F A379134 Equals the largest root of 1744*x^4 - 3816*x^2 + 361.
%e A379134 1.4453319256522148283158512491020811977238711778430...
%t A379134 First[RealDigits[Sqrt[477/436 + 97*Sqrt[5]/218], 10, 100]] (* or *)
%t A379134 First[RealDigits[PolyhedronData["PentakisDodecahedron", "Inradius"], 10, 100]]
%o A379134 (PARI) sqrt(477/436 + 97*sqrt(5)/218) \\ _Charles R Greathouse IV_, Feb 05 2025
%Y A379134 Cf. A379132 (surface area), A379133 (volume), A379135 (midradius), A379136 (dihedral angle).
%Y A379134 Cf. A002163.
%K A379134 nonn,cons,easy
%O A379134 1,2
%A A379134 _Paolo Xausa_, Dec 17 2024