A377970 - OEIS

%I #7 Nov 13 2024 16:31:59

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

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

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

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

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

%F Equals arcsec(sqrt(12*A377604^2 - 3)) + arcsec(sqrt(4*A377604^2 - 1)).

%F Equals Pi - arccos(sqrt(1 - 2/(3*A058265))).

%F Equals Pi - arccos(c), where c is the positive real root of 27*x^6 - 99*x^4 + 129*x^2 - 49.

%e 2.4955316305777334348382341626778898107867306036053...

%t First[RealDigits[Pi - ArcCos[Root[27*#^6 - 99*#^4 + 129*#^2 - 49 &, 2]], 10, 100]] (* or *)

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

%Y Cf. A058265, A377602, A377603, A377604, A377605, A377969.

%K nonn,cons,easy

%O 1,1

%A _Paolo Xausa_, Nov 13 2024