A390144 - OEIS

%I #5 Oct 30 2025 18:32:11

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

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

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

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

%H Paolo Xausa, <a href="/A390144/b390144.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 largest negative root of 27*x^3 + 27*x^2 - 75*x - 43.

%e 2.1248189366147042378417781962115166356186320982755...

%t First[RealDigits[ArcCos[Root[27*#^3 + 27*#^2 - 75*# - 43 &, 2]], 10, 100]] (* or *)

%t First[RealDigits[RankedMin[Union[PolyhedronData["J84", "DihedralAngles"]], 2], 10, 100]]

%Y Cf. other J_84 dihedral angles: A390143, A390145.

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

%K nonn,cons,easy

%O 1,1

%A _Paolo Xausa_, Oct 28 2025