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A379888 Decimal expansion of the surface area of a pentagonal hexecontahedron with unit shorter edge length.

%I A379888 #10 Feb 07 2025 13:47:20
%S A379888 1,6,2,6,9,8,9,6,4,1,9,8,4,6,6,6,2,6,7,6,8,7,2,5,8,2,4,1,2,1,3,7,9,5,
%T A379888 9,7,0,9,7,1,8,2,2,3,6,6,4,0,3,8,2,5,8,8,3,1,8,7,7,7,1,4,4,7,4,9,3,6,
%U A379888 4,3,1,2,8,5,5,8,2,0,1,5,3,5,7,4,1,9,8,0,4,3
%N A379888 Decimal expansion of the surface area of a pentagonal hexecontahedron with unit shorter edge length.
%C A379888 The pentagonal hexecontahedron is the dual polyhedron of the snub dodecahedron.
%H A379888 Paolo Xausa, <a href="/A379888/b379888.txt">Table of n, a(n) for n = 3..10000</a>
%H A379888 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentagonalHexecontahedron.html">Pentagonal Hexecontahedron</a>.
%H A379888 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentagonal_hexecontahedron">Pentagonal hexecontahedron</a>.
%H A379888 <a href="/index/Al#algebraic_12">Index entries for algebraic numbers, degree 12</a>.
%F A379888 Equals 30*(2 + 3*t)*sqrt(1 - t^2)/(1 - 2*t^2), 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 A379888 Equals the largest real root of 961*x^12 - 33925050*x^10 + 238487439375*x^8 - 374285139187500*x^6 + 215543322643359375*x^4 - 200764566730722656250*x^2 + 19088214930090087890625.
%e A379888 162.69896419846662676872582412137959709718223664038...
%t A379888 First[RealDigits[Root[961*#^12 - 33925050*#^10 + 238487439375*#^8 - 374285139187500*#^6 + 215543322643359375*#^4 - 200764566730722656250*#^2 + 19088214930090087890625 &, 8], 10, 100]]  (* or *)
%t A379888 First[RealDigits[PolyhedronData["PentagonalHexecontahedron", "SurfaceArea"], 10, 100]]
%Y A379888 Cf. A379889 (volume), A379890 (inradius), A379891 (midradius), A379892 (dihedral angle).
%Y A379888 Cf. A377804 (surface area of a snub dodecahedron with unit edge length).
%Y A379888 Cf. A001622.
%K A379888 nonn,cons,easy
%O A379888 3,2
%A A379888 _Paolo Xausa_, Jan 07 2025