A387607 - OEIS

%I #13 Nov 24 2025 08:40:10

%S 2,7,7,8,3,2,8,6,6,6,1,9,9,0,2,1,3,5,5,1,0,7,4,2,8,9,1,9,0,0,5,0,7,8,

%T 0,0,4,2,5,0,8,3,3,3,3,6,4,0,9,0,3,0,2,5,4,1,8,9,6,7,8,8,2,2,4,6,8,6,

%U 4,2,9,7,3,5,1,3,1,6,6,8,6,6,6,8,4,5,7,9,1,6

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

%C This is the dihedral angle between triangular faces in the antiprism part of the solid.

%C Also the analogous dihedral angle in a gyroelongated pentagonal rotunda, gyroelongated pentagonal bicupola, gyroelongated pentagonal cupolarotunda and gyroelongated pentagonal birotunda (Johnson solids J_25, J_46, J_47 and J_48, respectively).

%C Also the analogous dihedral angle in a decagonal antiprism.

%H Paolo Xausa, <a href="/A387607/b387607.txt">Table of n, a(n) for n = 1..10000</a>

%H Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Decagonal_antiprism">Decagonal antiprism</a>.

%H Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Gyroelongated_pentagonal_bicupola">Gyroelongated pentagonal bicupola</a>.

%H Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Gyroelongated_pentagonal_birotunda">Gyroelongated pentagonal birotunda</a>.

%H Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Gyroelongated_pentagonal_cupola">Gyroelongated pentagonal cupola</a>.

%H Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Gyroelongated_pentagonal_cupolarotunda">Gyroelongated pentagonal cupolarotunda</a>.

%H Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Gyroelongated_pentagonal_rotunda">Gyroelongated pentagonal rotunda</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Gyroelongated_pentagonal_bicupola">Gyroelongated pentagonal bicupola</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Gyroelongated_pentagonal_birotunda">Gyroelongated pentagonal birotunda</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Gyroelongated_pentagonal_cupola">Gyroelongated pentagonal cupola</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Gyroelongated_pentagonal_cupolarotunda">Gyroelongated pentagonal cupolarotunda</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Gyroelongated_pentagonal_rotunda">Gyroelongated pentagonal rotunda</a>.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals arccos((1 - sqrt(10 + 2*sqrt(5)))/3) = arccos((1 - sqrt(10 + A010476))/3).

%e 2.7783286661990213551074289190050780042508333364090...

%t First[RealDigits[ArcCos[(1 - Sqrt[10 + Sqrt[20]])/3], 10, 100]] (* or *)

%t First[RealDigits[Max[PolyhedronData["J24", "DihedralAngles"]], 10, 100]]

%Y Cf. other J_24 dihedral angles: A377995, A377996, A387608, A387609, A387610.

%Y Cf. A384283 (J_24 volume), A384284 (J_24 surface area).

%Y Cf. A384285 (J_25 volume), A384286 (J_25 surface area).

%Y Cf. A385260 (J_46 volume), A385261 (J_46 surface area).

%Y Cf. A385262 (J_47 volume), A385263 (J_47 surface area).

%Y Cf. A385264 (J_48 volume), A385488 (J_48 surface area).

%Y Cf. A010476.

%K nonn,cons,easy

%O 1,1

%A _Paolo Xausa_, Sep 04 2025