A391146 - OEIS

%I #10 Dec 10 2025 08:59:50

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

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

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

%N Decimal expansion of the second smallest dihedral angle, in radians, in a disphenocingulum (Johnson solid J_90).

%H Paolo Xausa, <a href="/A391146/b391146.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%F Equals arccos(c), where c = -0.569307... is the largest negative real root of 531441*x^12 + 17714700*x^11 + 194743602*x^10 + 814167612*x^9 + 1478160495*x^8 + 1155453336*x^7 - 96884100*x^6 - 1588339368*x^5 - 2042658081*x^4 - 706449060*x^3 + 612044658*x^2 + 580836204*x + 135375265.

%e 2.176459066501222579898433924084539147055398826233...

%t First[RealDigits[ArcCos[Root[531441*#^12 + 17714700*#^11 + 194743602*#^10 + 814167612*#^9 + 1478160495*#^8 + 1155453336*#^7 - 96884100*#^6 - 1588339368*#^5 - 2042658081*#^4 - 706449060*#^3 + 612044658*#^2 + 580836204*# + 135375265 &, 6]], 10, 100]] (* or *)

%t First[RealDigits[RankedMin[Union[PolyhedronData["J90", "DihedralAngles"]], 2], 10, 100]]

%Y Cf. other J_90 dihedral angles: A391145, A391147, A391148, A391149, A391150, A391151.

%Y Cf. A386752 (J_90 volume), A385257 (J_90 surface area + 2).

%K nonn,cons,easy

%O 1,1

%A _Paolo Xausa_, Dec 07 2025