A377997 - OEIS

%I #6 Nov 16 2024 07:25:44

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

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

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

%N Decimal expansion of the dihedral angle, in radians, between triangular faces in a snub dodecahedron.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SnubDodecahedron.html">Snub Dodecahedron</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Snub_dodecahedron">Snub dodecahedron</a>.

%F Equals Pi - arccos((2/3)*A377849 + 1/3).

%F Equals Pi - arccos(c), where c is the largest real root of 729*x^6 + 486*x^5 - 729*x^4 - 756*x^3 + 63*x^2 + 270*x + 1.

%e 2.8654006883447286076046073417336569141190096726652...

%t First[RealDigits[Pi - ArcCos[2*Root[#^3 + 2*#^2 - GoldenRatio^2 &, 1]/3 + 1/3], 10, 100]] (* or *)

%t First[RealDigits[Max[PolyhedronData["SnubDodecahedron", "DihedralAngles"]], 10, 100]]

%Y Cf. A377804, A377805, A377806, A377807, A377849, A377998.

%K nonn,cons,easy

%O 1,1

%A _Paolo Xausa_, Nov 15 2024