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Decimal expansion of the volume of a triakis icosahedron with unit shorter edge length.
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%I #9 Dec 15 2024 07:24:42

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

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

%U 1,9,3,0,0,8,3,2,2,8,6,5,9,2,3,0,9,6,8,4,6,8

%N Decimal expansion of the volume of a triakis icosahedron with unit shorter edge length.

%C The triakis icosahedron is the dual polyhedron of the truncated dodecahedron.

%H Paolo Xausa, <a href="/A378974/b378974.txt">Table of n, a(n) for n = 2..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 (19 + 13*sqrt(5))/4 = (19 + 13*A002163)/4.

%e 12.017220926874316513329814423376647765182009668737...

%t First[RealDigits[(19 + 13*Sqrt[5])/4, 10, 100]] (* or *)

%t First[RealDigits[PolyhedronData["TriakisIcosahedron", "Volume"], 10, 100]]

%Y Cf. A378973 (surface area), A378975 (inradius), A378976 (midradius), A378977 (dihedral angle).

%Y Cf. A377695 (volume of a truncated dodecahedron with unit edge length).

%Y Cf. A002163.

%K nonn,cons,easy,new

%O 2,2

%A _Paolo Xausa_, Dec 14 2024