A391145 - OEIS

%I #10 Dec 10 2025 08:59:55

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

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

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

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

%H Paolo Xausa, <a href="/A391145/b391145.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 = -0.176980... is the largest negative real root of 16*x^12 + 352*x^11 + 2264*x^10 + 3416*x^9 - 911*x^8 - 2320*x^7 - 1368*x^6 - 2768*x^5 - 440*x^4 + 1280*x^3 + 800*x^2 + 192*x + 16.

%e 1.74871378602598722798456259406830020257739824600...

%t First[RealDigits[ArcCos[Root[16*#^12 + 352*#^11 + 2264*#^10 + 3416*#^9 - 911*#^8 - 2320*#^7 - 1368*#^6 - 2768*#^5 - 440*#^4 + 1280*#^3 + 800*#^2 + 192*# + 16 &, 6]], 10, 100]] (* or *)

%t First[RealDigits[Min[PolyhedronData["J90", "DihedralAngles"]], 10, 100]]

%Y Cf. other J_90 dihedral angles: A391146, A391147, A391148, A391149, A391150, A391151.

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

%K nonn,cons,easy

%O 1,2

%A _Paolo Xausa_, Dec 05 2025