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%I A387609 #10 Sep 05 2025 11:34:23
%S A387609 2,2,1,5,9,4,1,9,0,6,4,8,7,8,0,7,1,4,6,9,8,6,9,3,5,8,8,9,9,1,9,6,2,8,
%T A387609 9,1,6,8,0,3,7,5,9,1,9,9,9,7,5,9,1,2,1,8,4,1,5,8,5,5,2,7,5,0,5,2,6,9,
%U A387609 3,4,1,5,2,3,0,6,8,2,0,5,4,7,3,6,8,1,8,3,8,3
%N A387609 Decimal expansion of the fifth largest (second smallest) dihedral angle, in radians, in a gyroelongated pentagonal cupola (Johnson solid J_24).
%C A387609 This is the dihedral angle between a triangular face and a square face at the edge where the antiprism and cupola parts of the solid meet.
%C A387609 Also the analogous dihedral angle in a gyroelongated pentagonal bicupola and gyroelongated pentagonal cupolarotunda (Johnson solids J_46 and J_47, respectively).
%H A387609 Paolo Xausa,
Table of n, a(n) for n = 1..10000
%H A387609 Polytope Wiki,
Gyroelongated pentagonal bicupola.
%H A387609 Polytope Wiki,
Gyroelongated pentagonal cupola.
%H A387609 Polytope Wiki,
Gyroelongated pentagonal cupolarotunda.
%H A387609 Wikipedia,
Gyroelongated pentagonal bicupola.
%H A387609 Wikipedia,
Gyroelongated pentagonal cupola.
%H A387609 Wikipedia,
Gyroelongated pentagonal cupolarotunda.
%F A387609 Equals arctan(2)/2 + arccos((sqrt(5 + 2*sqrt(5)) - sqrt(5) - 1)/sqrt(3)) = A195693 + arccos((sqrt(5 + A010476) - A002163 - 1)/A002194).
%F A387609 Equals A195693 + A387610.
%e A387609 2.2159419064878071469869358899196289168037591999759...
%t A387609 First[RealDigits[ArcTan[2]/2 + ArcCos[(Sqrt[5 + Sqrt[20]] - Sqrt[5] - 1)/Sqrt[3]], 10, 100]] (* or *)
%t A387609 First[RealDigits[RankedMax[Union[PolyhedronData["J24", "DihedralAngles"]], 5], 10, 100]]
%Y A387609 Cf. other J_24 dihedral angles: A377995, A377996, A387607, A387608, A387610.
%Y A387609 Cf. A384283 (J_24 volume), A384284 (J_24 surface area).
%Y A387609 Cf. A385260 (J_46 volume), A385261 (J_46 surface area).
%Y A387609 Cf. A385262 (J_47 volume), A385263 (J_47 surface area).
%Y A387609 Cf. A002163, A002194, A010476, A195693.
%K A387609 nonn,cons,easy
%O A387609 1,1
%A A387609 _Paolo Xausa_, Sep 05 2025
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