A387149 - OEIS

%I #10 Aug 22 2025 02:44:01

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

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

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

%N Decimal expansion of the second largest dihedral angle, in radians, in a gyroelongated square pyramid (Johnson solid J_10).

%C This is the dihedral angle between adjacent triangular faces in the square antiprism part of the solid.

%C Also the analogous dihedral angle in a gyroelongated square bipyramid (Johnson solid J_17).

%H Paolo Xausa, <a href="/A387149/b387149.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Gyroelongated_square_bipyramid">Gyroelongated square bipyramid</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Gyroelongated_square_pyramid">Gyroelongated square pyramid</a>.

%F Equals arccos((1 - 2*sqrt(2))/3) = arccos((1 - A010466)/3).

%e 2.2261954369024298095991888315497640747046712455090...

%t First[RealDigits[ArcCos[(1 - Sqrt[8])/3], 10, 100]] (* or *)

%t First[RealDigits[RankedMax[Union[PolyhedronData["J10", "DihedralAngles"]], 2], 10, 100]]

%Y Cf. other J_10 dihedral angles: A156546, A387148, A387150.

%Y Cf. A179638 (J_10 volume), A374948 (J_10 surface area).

%Y Cf. A010466.

%K nonn,cons,easy

%O 1,1

%A _Paolo Xausa_, Aug 19 2025