%I #8 Nov 16 2024 07:25:43

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

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

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

%N Decimal expansion of the dihedral angle, in radians, between triangular and pentagonal 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(sqrt((12*phi - (4*phi + 8)*xi*(xi + 1) + 19)/15)), where phi = A001622 and xi = A377849.

%F Equals Pi - arccos(c), where c is the real root closest to 9/10 of 91125*x^12 - 668250*x^10 + 2006775*x^8 - 2735100*x^6 + 1768275*x^4 - 502410*x^2 + 43681.

%e 2.669130633625756107707940935718208230518703745355...

%t First[RealDigits[Pi - ArcCos[Root[91125*#^12 - 668250*#^10 + 2006775*#^8 - 2735100*#^6 + 1768275*#^4 - 502410*#^2 + 43681&, 7]], 10, 100]] (* or *)

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

%Y Cf. A001622, A377804, A377805, A377806, A377807, A377849, A377997.

%K nonn,cons,easy,new

%O 1,1

%A _Paolo Xausa_, Nov 15 2024