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%I #6 Nov 16 2024 07:25:46
%S 2,7,7,6,7,2,8,8,2,5,4,7,6,3,1,0,0,5,6,7,3,5,2,4,5,0,5,3,3,7,2,8,4,2,
%T 5,3,6,4,9,8,9,1,6,4,4,2,3,5,1,2,4,8,9,7,5,6,2,0,4,6,9,8,4,6,5,7,6,9,
%U 0,6,9,5,6,4,5,2,8,2,5,4,2,9,2,3,0,2,9,3,1,2
%N Decimal expansion of the dihedral angle, in radians, between triangular and square faces in a (small) rhombicosidodecahedron.
%C Also the dihedral angle, in radians, between square and hexagonal faces in a truncated icosidodecahedron (great rhombicosidodecahedron).
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GreatRhombicosidodecahedron.html">Great Rhombicosidodecahedron</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmallRhombicosidodecahedron.html">Small Rhombicosidodecahedron</a>.
%F Equals arccos(-(sqrt(3) + sqrt(15))/6) = arccos(-(A002194 + A010472)/6).
%e 2.7767288254763100567352450533728425364989164423512...
%t First[RealDigits[ArcCos[-(Sqrt[3] + Sqrt[15])/6], 10, 100]] (* or *)
%t First[RealDigits[Max[PolyhedronData["Rhombicosidodecahedron", "DihedralAngles"]], 10, 100]]
%Y Cf. A002194, A010472, A377995.
%K nonn,cons,easy
%O 1,1
%A _Paolo Xausa_, Nov 15 2024