cp's OEIS Frontend

A386853 Decimal expansion of the dihedral angle, in radians, between the 10-gonal face and a triangular face in a pentagonal rotunda (Johnson solid J_6).

%I A386853 #15 Aug 19 2025 10:48:35
%S A386853 1,3,8,2,0,8,5,7,9,6,0,1,1,3,3,4,5,4,9,4,5,0,1,8,7,2,9,1,4,5,7,1,4,3,
%T A386853 2,6,9,7,6,1,8,1,3,8,3,4,0,1,0,6,9,3,4,3,2,5,0,3,6,7,7,4,3,8,1,6,7,9,
%U A386853 6,2,4,8,3,4,8,7,8,0,6,6,7,1,7,0,5,0,5,0,5,5
%N A386853 Decimal expansion of the dihedral angle, in radians, between the 10-gonal face and a triangular face in a pentagonal rotunda (Johnson solid J_6).
%H A386853 Paolo Xausa, <a href="/A386853/b386853.txt">Table of n, a(n) for n = 1..10000</a>
%H A386853 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentagonal_rotunda">Pentagonal rotunda</a>.
%H A386853 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A386853 Equals arccos(sqrt((5 - 2*sqrt(5))/15)) = arccos(sqrt((5 - A010476)/15)).
%e A386853 1.38208579601133454945018729145714326976181383401...
%t A386853 First[RealDigits[ArcCos[Sqrt[(5 - Sqrt[20])/15]], 10, 100]] (* or *)
%t A386853 First[RealDigits[RankedMin[Union[PolyhedronData["J6", "DihedralAngles"]], 2], 10, 100]]
%o A386853 (PARI) acos(sqrt((5 - 2*sqrt(5))/15)) \\ _Charles R Greathouse IV_, Aug 19 2025
%Y A386853 Cf. A179593 (volume), A179637 (surface area).
%Y A386853 Cf. other J_6 dihedral angles: A105199, A344075.
%Y A386853 Cf. A010476, A386852.
%K A386853 nonn,cons,easy
%O A386853 1,2
%A A386853 _Paolo Xausa_, Aug 06 2025