A390145 - OEIS

%I #6 Oct 30 2025 18:33:56

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

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

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

%N Decimal expansion of the largest dihedral angle, in radians, in a snub disphenoid (Johnson solid J_84).

%H Paolo Xausa, <a href="/A390145/b390145.txt">Table of n, a(n) for n = 1..10000</a>

%H Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Snub_disphenoid">Snub disphenoid</a>.

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

%F Equals arccos(c), where c is the smallest root of 27*x^3 - 45*x^2 - 24*x + 44.

%e 2.904935646441255214401380074990057843793815602886...

%t First[RealDigits[ArcCos[Root[27*#^3 - 45*#^2 - 24*# + 44 &, 1]], 10, 100]] (* or *)

%t First[RealDigits[Max[PolyhedronData["J84", "DihedralAngles"]], 10, 100]]

%Y Cf. other J_84 dihedral angles: A390143, A390144.

%Y Cf. A386695 (J_84 volume), A010482 (J_84 surface area).

%K nonn,cons,easy

%O 1,1

%A _Paolo Xausa_, Oct 28 2025