cp's OEIS Frontend

A387610 Decimal expansion of the smallest dihedral angle, in radians, in a gyroelongated pentagonal cupola (Johnson solid J_24).

%I A387610 #7 Sep 05 2025 11:34:19
%S A387610 1,6,6,2,3,6,7,5,4,7,5,9,0,7,6,1,8,9,5,4,7,8,4,0,3,1,5,9,8,3,0,3,6,0,
%T A387610 3,9,6,7,6,8,7,3,5,3,7,7,2,7,5,1,9,5,8,6,0,8,2,0,2,8,3,1,4,6,8,1,0,0,
%U A387610 7,8,9,8,2,8,1,8,1,3,9,1,5,0,3,6,1,4,7,5,2,6
%N A387610 Decimal expansion of the smallest dihedral angle, in radians, in a gyroelongated pentagonal cupola (Johnson solid J_24).
%C A387610 This is the dihedral angle between a triangular face and the decagonal face.
%C A387610 Also the analogous dihedral angle in a gyroelongated pentagonal rotunda (Johnson solid J_25).
%C A387610 Also the analogous dihedral angle in a decagonal antiprism.
%H A387610 Paolo Xausa, <a href="/A387610/b387610.txt">Table of n, a(n) for n = 1..10000</a>
%H A387610 Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Decagonal_antiprism">Decagonal antiprism</a>.
%H A387610 Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Gyroelongated_pentagonal_cupola">Gyroelongated pentagonal cupola</a>.
%H A387610 Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Gyroelongated_pentagonal_rotunda">Gyroelongated pentagonal rotunda</a>.
%H A387610 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gyroelongated_pentagonal_cupola">Gyroelongated pentagonal cupola</a>.
%H A387610 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gyroelongated_pentagonal_rotunda">Gyroelongated pentagonal rotunda</a>.
%F A387610 Equals arccos((sqrt(5 + 2*sqrt(5)) - sqrt(5) - 1)/sqrt(3)) = arccos((sqrt(5 + A010476) - A002163 - 1)/A002194).
%F A387610 Equals A387608 - A386852.
%F A387610 Equals A387609 - A195693.
%e A387610 1.662367547590761895478403159830360396768735377275...
%t A387610 First[RealDigits[ArcCos[(Sqrt[5 + Sqrt[20]] - Sqrt[5] - 1)/Sqrt[3]], 10, 100]] (* or *)
%t A387610 First[RealDigits[Min[PolyhedronData["J24", "DihedralAngles"]], 10, 100]]
%Y A387610 Cf. other J_24 dihedral angles: A377995, A377996, A387607, A387608, A387609.
%Y A387610 Cf. A384283 (J_24 volume), A384284 (J_24 surface area).
%Y A387610 Cf. A384285 (J_25 volume), A384286 (J_25 surface area).
%Y A387610 Cf. A002163, A002194, A010476, A195693, A386852.
%K A387610 nonn,cons,easy,new
%O A387610 1,2
%A A387610 _Paolo Xausa_, Sep 05 2025