cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A387609 Decimal expansion of the fifth largest (second smallest) dihedral angle, in radians, in a gyroelongated pentagonal cupola (Johnson solid J_24).

This page as a plain text file.
%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, <a href="/A387609/b387609.txt">Table of n, a(n) for n = 1..10000</a>
%H A387609 Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Gyroelongated_pentagonal_bicupola">Gyroelongated pentagonal bicupola</a>.
%H A387609 Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Gyroelongated_pentagonal_cupola">Gyroelongated pentagonal cupola</a>.
%H A387609 Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Gyroelongated_pentagonal_cupolarotunda">Gyroelongated pentagonal cupolarotunda</a>.
%H A387609 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gyroelongated_pentagonal_bicupola">Gyroelongated pentagonal bicupola</a>.
%H A387609 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gyroelongated_pentagonal_cupola">Gyroelongated pentagonal cupola</a>.
%H A387609 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gyroelongated_pentagonal_cupolarotunda">Gyroelongated pentagonal cupolarotunda</a>.
%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,new
%O A387609 1,1
%A A387609 _Paolo Xausa_, Sep 05 2025