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A379889 Decimal expansion of the volume of a pentagonal hexecontahedron with unit shorter edge length.

%I A379889 #8 Feb 10 2025 11:55:21
%S A379889 1,8,9,7,8,9,8,5,2,0,6,6,8,8,5,2,7,9,1,0,6,3,2,3,0,8,6,1,9,4,4,7,3,7,
%T A379889 9,6,9,9,1,0,6,0,3,3,6,2,9,7,3,6,1,1,5,6,6,1,4,6,7,9,8,0,6,7,5,5,7,5,
%U A379889 7,4,0,4,9,5,6,8,6,8,1,3,6,9,9,0,1,0,4,0,1,9
%N A379889 Decimal expansion of the volume of a pentagonal hexecontahedron with unit shorter edge length.
%C A379889 The pentagonal hexecontahedron is the dual polyhedron of the snub dodecahedron.
%H A379889 Paolo Xausa, <a href="/A379889/b379889.txt">Table of n, a(n) for n = 3..10000</a>
%H A379889 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentagonalHexecontahedron.html">Pentagonal Hexecontahedron</a>.
%H A379889 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentagonal_hexecontahedron">Pentagonal hexecontahedron</a>.
%H A379889 <a href="/index/Al#algebraic_12">Index entries for algebraic numbers, degree 12</a>.
%F A379889 Equals 5*(1 + t)*(2 + 3*t)/((1 - 2*t^2)*sqrt(1 - 2*t)), where t = ((44 + 12*A001622*(9 + sqrt(81*A001622 - 15)))^(1/3) + (44 + 12*A001622*(9 - sqrt(81*A001622 - 15)))^(1/3) - 4)/12.
%F A379889 Equals the largest real root of 3936256*x^12 - 143719449600*x^10 + 69717538560000*x^8 - 965464153000000*x^6 - 5195593956250000*x^4 - 6093827421875000*x^2 + 171855712890625.
%e A379889 189.78985206688527910632308619447379699106033629736...
%t A379889 First[RealDigits[Root[3936256*#^12 - 143719449600*#^10 + 69717538560000*#^8 - 965464153000000*#^6 - 5195593956250000*#^4 - 6093827421875000*#^2 + 171855712890625 &, 8], 10, 100]] (* or *)
%t A379889 First[RealDigits[PolyhedronData["PentagonalHexecontahedron", "Volume"], 10, 100]]
%Y A379889 Cf. A379888 (surface area), A379890 (inradius), A379891 (midradius), A379892 (dihedral angle).
%Y A379889 Cf. A377805 (volume of a snub dodecahedron with unit edge length).
%Y A379889 Cf. A001622.
%K A379889 nonn,cons,easy
%O A379889 3,2
%A A379889 _Paolo Xausa_, Jan 07 2025