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A379892 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a pentagonal hexecontahedron.

%I A379892 #10 Feb 10 2025 08:42:30
%S A379892 2,6,7,3,4,7,3,2,2,7,1,7,6,7,8,4,6,6,8,2,7,9,0,7,0,3,3,4,8,9,5,7,9,1,
%T A379892 7,1,9,7,8,7,0,3,1,7,5,0,2,6,9,3,4,4,5,6,5,7,6,9,9,5,2,4,5,0,0,2,2,5,
%U A379892 5,7,4,0,0,5,4,0,2,1,6,0,5,9,9,6,7,4,7,4,7,5
%N A379892 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a pentagonal hexecontahedron.
%C A379892 The pentagonal hexecontahedron is the dual polyhedron of the snub dodecahedron.
%H A379892 Paolo Xausa, <a href="/A379892/b379892.txt">Table of n, a(n) for n = 1..10000</a>
%H A379892 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentagonalHexecontahedron.html">Pentagonal Hexecontahedron</a>.
%H A379892 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentagonal_hexecontahedron">Pentagonal hexecontahedron</a>.
%H A379892 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A379892 Equals arccos(A377849/(A377849 - 2)).
%F A379892 Equals arccos(c), where c is the smallest real root of 209*x^6 - 94*x^5 - 137*x^4 + 100*x^3 - 9*x^2 - 6*x + 1.
%e A379892 2.6734732271767846682790703348957917197870317502693...
%t A379892 First[RealDigits[ArcCos[#/(# - 2)] & [Root[#^3 + 2*#^2 - GoldenRatio^2 &, 1]], 10, 100]] (* or *)
%t A379892 First[RealDigits[First[PolyhedronData["PentagonalHexecontahedron", "DihedralAngles"]], 10, 100]]
%o A379892 (PARI) acos(polrootsreal(209*x^6 - 94*x^5 - 137*x^4 + 100*x^3 - 9*x^2 - 6*x + 1)[1]) \\ _Charles R Greathouse IV_, Feb 10 2025
%Y A379892 Cf. A379888 (surface area), A379889 (volume), A379890 (inradius), A379891 (midradius).
%Y A379892 Cf. A377997 and A377998 (dihedral angles of a snub dodecahedron).
%Y A379892 Cf. A377849.
%K A379892 nonn,cons,easy
%O A379892 1,1
%A A379892 _Paolo Xausa_, Jan 10 2025