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%I #7 Dec 15 2024 07:24:55
%S 2,8,0,3,2,1,7,8,5,6,0,8,4,8,0,5,9,6,2,1,0,3,4,4,9,3,2,6,4,8,7,7,2,5,
%T 3,2,8,1,1,5,2,6,5,9,8,8,0,3,5,4,0,1,2,6,9,8,4,7,0,1,7,0,6,0,5,1,6,8,
%U 7,6,1,6,4,9,4,7,8,1,9,2,7,5,1,4,3,8,7,6,5,3
%N Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a triakis icosahedron.
%C The triakis icosahedron is the dual polyhedron of the truncated dodecahedron.
%H Paolo Xausa, <a href="/A378977/b378977.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriakisIcosahedron.html">Triakis Icosahedron</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Triakis_icosahedron">Triakis icosahedron</a>.
%F Equals arccos(-3*(8 + 5*sqrt(5))/61 = arccos(-3*(8 + 5*A002163)/61.
%e 2.8032178560848059621034493264877253281152659880354...
%t First[RealDigits[ArcCos[-3*(8 + 5*Sqrt[5])/61], 10, 100]] (* or *)
%t First[RealDigits[First[PolyhedronData["TriakisIcosahedron", "DihedralAngles"]], 10, 100]]
%Y Cf. A378973 (surface area), A378974 (volume), A378975 (inradius), A378976 (midradius).
%Y Cf. A137218 and A344075 (dihedral angles of a truncated dodecahedron).
%Y Cf. A002163.
%K nonn,cons,easy
%O 1,1
%A _Paolo Xausa_, Dec 14 2024