cp's OEIS Frontend

A387608 Decimal expansion of the fourth largest dihedral angle, in radians, in a gyroelongated pentagonal cupola (Johnson solid J_24).

%I A387608 #15 Sep 05 2025 11:34:43
%S A387608 2,3,1,4,7,2,5,6,8,7,3,7,5,1,3,0,0,8,1,4,7,3,7,9,3,7,9,1,4,7,4,1,8,2,
%T A387608 9,7,1,1,3,4,0,4,3,2,9,7,2,3,8,1,7,5,6,0,2,6,1,5,0,1,1,0,9,3,5,1,6,2,
%U A387608 2,2,5,6,6,6,3,9,1,7,8,6,8,3,2,7,1,0,4,2,4,1
%N A387608 Decimal expansion of the fourth largest dihedral angle, in radians, in a gyroelongated pentagonal cupola (Johnson solid J_24).
%C A387608 This is the dihedral angle between adjacent triangular faces at the edge where the antiprism and cupola parts of the solid meet.
%C A387608 Also the analogous dihedral angle in a gyroelongated pentagonal bicupola and gyroelongated pentagonal cupolarotunda (Johnson solids J_46 and J_47, respectively).
%H A387608 Paolo Xausa, <a href="/A387608/b387608.txt">Table of n, a(n) for n = 1..10000</a>
%H A387608 Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Gyroelongated_pentagonal_bicupola">Gyroelongated pentagonal bicupola</a>.
%H A387608 Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Gyroelongated_pentagonal_cupola">Gyroelongated pentagonal cupola</a>.
%H A387608 Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Gyroelongated_pentagonal_cupolarotunda">Gyroelongated pentagonal cupolarotunda</a>.
%H A387608 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gyroelongated_pentagonal_bicupola">Gyroelongated pentagonal bicupola</a>.
%H A387608 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gyroelongated_pentagonal_cupola">Gyroelongated pentagonal cupola</a>.
%H A387608 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gyroelongated_pentagonal_cupolarotunda">Gyroelongated pentagonal cupolarotunda</a>.
%F A387608 Equals arccos(sqrt((5 + 2*sqrt(5))/15)) + arccos((sqrt(5 + 2*sqrt(5)) - sqrt(5) - 1)/sqrt(3)) = arccos(sqrt((5 + A010476)/15)) + arccos((sqrt(5 + A010476) - A002163 - 1)/A002194).
%F A387608 Equals A386852 + A387610.
%e A387608 2.314725687375130081473793791474182971134043297238...
%t A387608 First[RealDigits[ArcSec[Sqrt[15 - 6*#]] + ArcCos[(Sqrt[5 + 2*#] - # - 1)/Sqrt[3]] & [Sqrt[5]], 10, 100]] (* or *)
%t A387608 First[RealDigits[RankedMax[Union[PolyhedronData["J24", "DihedralAngles"]],4], 10, 100]]
%Y A387608 Cf. other J_24 dihedral angles: A377995, A377996, A387607, A387609, A387610.
%Y A387608 Cf. A384283 (J_24 volume), A384284 (J_24 surface area).
%Y A387608 Cf. A385260 (J_46 volume), A385261 (J_46 surface area).
%Y A387608 Cf. A385262 (J_47 volume), A385263 (J_47 surface area).
%Y A387608 Cf. A002163, A002194, A010476, A386852.
%K A387608 nonn,cons,easy,new
%O A387608 1,1
%A A387608 _Paolo Xausa_, Sep 04 2025