cp's OEIS Frontend

A387321 Decimal expansion of the second largest dihedral angle, in radians, in a gyroelongated square cupola (Johnson solid J_23).

%I A387321 #14 Sep 02 2025 04:01:23
%S A387321 2,6,4,1,2,0,9,0,0,0,3,7,4,0,3,9,5,4,4,0,2,1,4,5,1,0,5,2,8,5,1,1,3,5,
%T A387321 8,3,2,6,7,9,8,7,1,6,7,8,2,5,4,8,2,9,5,2,6,2,7,5,0,5,3,7,4,4,6,2,4,5,
%U A387321 2,5,3,7,1,3,7,8,9,6,2,7,0,0,0,5,2,0,7,5,4,4
%N A387321 Decimal expansion of the second largest dihedral angle, in radians, in a gyroelongated square cupola (Johnson solid J_23).
%C A387321 This is the dihedral angle between adjacent triangular faces at the edge where the antiprism and cupola parts of the solid meet.
%C A387321 Also the analogous dihedral angle in a gyroelongated square bicupola (Johnson solid J_45).
%H A387321 Paolo Xausa, <a href="/A387321/b387321.txt">Table of n, a(n) for n = 1..10000</a>
%H A387321 Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Gyroelongated_square_bicupola">Gyroelongated square bicupola</a>.
%H A387321 Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Gyroelongated_square_cupola">Gyroelongated square cupola</a>.
%H A387321 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gyroelongated_square_bicupola">Gyroelongated square bicupola</a>.
%H A387321 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gyroelongated_square_cupola">Gyroelongated square cupola</a>.
%F A387321 Equals arcsec(sqrt(3)) + arccos(-sqrt((7 + 4*sqrt(2) - 2*sqrt(20 + 14*sqrt(2)))/3)) = A195696 + arccos(-sqrt((7 + A010487 - 2*sqrt(20 + 14*A002193))/3)).
%F A387321 Equals A195696 + A387323.
%e A387321 2.6412090003740395440214510528511358326798716782548...
%t A387321 First[RealDigits[ArcSec[Sqrt[3]] + ArcCos[-Sqrt[(7 + Sqrt[32] - 2*Sqrt[20 + 14*Sqrt[2]])/3]], 10, 100]] (* or *)
%t A387321 First[RealDigits[RankedMax[Union[PolyhedronData["J23", "DihedralAngles"]],2], 10, 100]]
%Y A387321 Cf. other J_23 dihedral angles: A177870, A195702, A387320, A387322, A387323.
%Y A387321 Cf. A384214 (J_23 volume), A384215 (J_23 surface area).
%Y A387321 Cf. A385258 (J_45 volume), A385259 (J_45 surface area).
%Y A387321 Cf. A002193, A010487, A195696.
%K A387321 nonn,cons,easy,new
%O A387321 1,1
%A A387321 _Paolo Xausa_, Aug 27 2025