A390638 - OEIS

%I #8 Nov 24 2025 10:35:48

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

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

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

%N Decimal expansion of the largest dihedral angle, in radians, in a sphenomegacorona (Johnson solid J_88).

%H Paolo Xausa, <a href="/A390638/b390638.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%F Equals arccos(c), where c = -0.9893886... is the smallest real root of 59049*x^16 - 314928*x^15 + 419904*x^14 + 542376*x^13 - 1641708*x^12 + 307152*x^11 + 1862352*x^10 - 1075032*x^9 - 609066*x^8 + 348720*x^7 - 71392*x^6 + 347416*x^5 - 64364*x^4 - 173520*x^3 + 52560*x^2 + 15000*x - 4375.

%e 2.9957832400120692992908056805273328034456543783317...

%t First[RealDigits[ArcCos[Root[59049*#^16 - 314928*#^15 + 419904*#^14 + 542376*#^13 - 1641708*#^12 + 307152*#^11 + 1862352*#^10 - 1075032*#^9 - 609066*#^8 + 348720*#^7 - 71392*#^6 + 347416*#^5 - 64364*#^4 - 173520*#^3 + 52560*#^2 + 15000*# - 4375 &, 1]], 10, 100]] (* or *)

%t First[RealDigits[Max[PolyhedronData["J88", "DihedralAngles"]], 10, 100]]

%Y Cf. other J_88 dihedral angles: A390630, A390631, A390632, A390633, A390634, A390635, A390636, A390637.

%Y Cf. A334114 (J_88 volume), A010502 (J_88 surface area - 2).

%K nonn,cons,easy

%O 1,1

%A _Paolo Xausa_, Nov 22 2025