A395170 - OEIS

%I #12 May 22 2026 07:56:14

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

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

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

%N Decimal expansion of the largest dihedral angle, in radians, in a uniform 9-gonal antiprism.

%C This is the dihedral angle between triangular faces.

%H Paolo Xausa, <a href="/A395170/b395170.txt">Table of n, a(n) for n = 1..10000</a>

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

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Antiprism.html">Antiprism</a>.

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

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%F Equals arccos((1 - 4*cos(Pi/9))/3) = arccos((1 - 4*A019879)/3).

%F Equals arccos(c), where c = -0.91959... is the smallest root of 27*(x^3 - x^2 - x) + 19.

%e 2.7378323668609414026808339410125045234685361092460...

%t First[RealDigits[ArcCos[(1 - 4*Cos[Pi/9])/3], 10, 100]]

%t (* Alternative: *)

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

%o (PARI) acos((1 - 4*cos(Pi/9))/3) \\ _Charles R Greathouse IV_, May 13 2026

%Y Cf. A395169 (the other dihedral angle).

%Y Cf. A395164 (volume), A395165 (surface area), A395166 (midradius), A395167 (circumradius), A395168 (height).

%Y Cf. A019879.

%K nonn,cons,easy

%O 1,1

%A _Paolo Xausa_, Apr 30 2026