A389932 - OEIS

%I #11 Oct 25 2025 05:41:10

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

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

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

%N Decimal expansion of the largest dihedral angle, in radians, in an augmented truncated cube (Johnson solid J_66).

%C This is the dihedral angle between a triangular face and a square face at the edge where the square cupola (Johnson solid J_4) and truncated cube parts of the solid meet.

%C Also the analogous dihedral angle in a biaugmented truncated cube (Johnson solid J_67).

%H Paolo Xausa, <a href="/A389932/b389932.txt">Table of n, a(n) for n = 1..10000</a>

%H Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Augmented_truncated_cube">Augmented truncated cube</a>.

%H Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Biaugmented_truncated_cube">Biaugmented truncated cube</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Augmented_truncated_cube">Augmented truncated cube</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Biaugmented_truncated_cube">Biaugmented truncated cube</a>.

%F Equals arccos(-1/sqrt(3) - 1/sqrt(6)) = arccos(-A020760 - A020763).

%e 2.9716741988627322699144471265836208510030470542...

%t First[RealDigits[ArcCos[-1/Sqrt[3] - 1/Sqrt[6]], 10, 100]] (* or *)

%t First[RealDigits[Max[PolyhedronData["J66", "DihedralAngles"]], 10, 100]]

%Y Cf. other J_66 dihedral angles: A019669, A177870, A195698, A195702.

%Y Cf. A386459 (J_66 volume), A386460 (J_66 surface area).

%Y Cf. A010524 (J_67 volume - 9), A386461 (J_67 surface area).

%Y Cf. A020760, A020763.

%K nonn,cons,easy

%O 1,1

%A _Paolo Xausa_, Oct 24 2025