cp's OEIS Frontend

A386692 Decimal expansion of the surface area of a parabidiminished rhombicosidodecahedron with unit edges.

%I A386692 #8 Jul 31 2025 08:43:23
%S A386692 5,6,9,2,3,3,1,8,7,1,0,6,8,8,1,2,9,4,7,4,2,6,0,1,8,8,5,0,7,8,3,5,3,2,
%T A386692 6,0,3,1,4,6,4,2,6,5,5,5,2,3,1,6,8,9,6,9,9,7,4,0,6,2,4,5,7,7,0,7,4,2,
%U A386692 8,3,8,9,0,6,8,3,7,1,1,6,9,9,8,3,0,0,2,4,6,4
%N A386692 Decimal expansion of the surface area of a parabidiminished rhombicosidodecahedron with unit edges.
%C A386692 The parabidiminished rhombicosidodecahedron is Johnson solid J_80.
%C A386692 Also the surface area of a metabidiminished rhombicosidodecahedron and a gyrate bidiminished rhombicosidodecahedron (Johnson solids J_81 and J_82, respectively) with unit edges.
%H A386692 Paolo Xausa, <a href="/A386692/b386692.txt">Table of n, a(n) for n = 2..10000</a>
%H A386692 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gyrate_bidiminished_rhombicosidodecahedron">Gyrate bidiminished rhombicosidodecahedron</a>.
%H A386692 Wikipedia, <a href="https://en.wikipedia.org/wiki/Metabidiminished_rhombicosidodecahedron">Metabidiminished rhombicosidodecahedron</a>.
%H A386692 Wikipedia, <a href="https://en.wikipedia.org/wiki/Parabidiminished_rhombicosidodecahedron">Parabidiminished rhombicosidodecahedron</a>.
%F A386692 Equals (5/2)*(8 + sqrt(3) + 2*sqrt(5 + 2*sqrt(5)) + sqrt(5*(5 + 2*sqrt(5)))) = (5/2)*(8 + A002194 + 2*sqrt(5 + A010476) + sqrt(5*(5 + A010476))).
%F A386692 Equals the largest root of x^8 - 160*x^7 + 9000*x^6 - 184000*x^5 - 828750*x^4 + 79100000*x^3 - 718984375*x^2 - 3800625000*x + 55781640625.
%e A386692 56.9233187106881294742601885078353260314642655523...
%t A386692 First[RealDigits[5/2*(8 + Sqrt[3] + 2*Sqrt[#] + Sqrt[5*#]) & [5 + Sqrt[20]], 10, 100]] (* or *)
%t A386692 First[RealDigits[PolyhedronData["J80", "SurfaceArea"], 10, 100]]
%Y A386692 Cf. A386691 (volume).
%Y A386692 Cf. A002194, A010476, A344149, A386690, A386694.
%K A386692 nonn,cons,easy
%O A386692 2,1
%A A386692 _Paolo Xausa_, Jul 30 2025