%I #9 Nov 16 2024 07:25:47

%S 2,5,8,8,0,1,8,2,9,4,6,9,2,7,4,7,9,8,6,9,5,4,1,1,0,6,5,3,1,9,0,2,3,4,

%T 3,6,4,1,6,2,1,4,5,5,7,6,6,7,4,3,8,9,4,9,7,6,3,6,6,7,4,9,8,8,5,9,0,9,

%U 6,1,2,3,6,7,9,7,5,2,7,6,0,1,6,2,1,3,2,6,2,6

%N Decimal expansion of the dihedral angle, in radians, between square and pentagonal faces in a (small) rhombicosidodecahedron.

%C Also the dihedral angle, in radians, between square and 10-gonal 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((5 + sqrt(5))/10)) = arccos(-sqrt(A242671)).

%e 2.588018294692747986954110653190234364162145576674...

%t First[RealDigits[ArcCos[-Sqrt[(5 + Sqrt[5])/10]], 10, 100]] (* or *)

%t First[RealDigits[Min[PolyhedronData["Rhombicosidodecahedron", "DihedralAngles"]], 10, 100]]

%Y Cf. A242671, A377996.

%K nonn,cons,easy,new

%O 1,1

%A _Paolo Xausa_, Nov 15 2024