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%I #19 Aug 21 2023 11:24:07
%S 7,2,0,5,6,2,1,7,3,1,0,5,6,0,1,6,3,6,0,0,5,2,7,9,2,3,2,4,0,9,7,2,5,7,
%T 0,7,7,7,9,0,4,4,4,5,0,9,3,5,5,8,9,3,3,5,0,1,1,0,2,2,8,3,4,2,6,9,5,2,
%U 3,3,6,2,4,1,1,4,5,6,7,5,1,6,2,6,8,4,5,0,7,3,0,2,1,8,5,2,1,5,7,8,6,0,9,1,7
%N Decimal expansion of the surface index of a regular tetrahedron.
%C Equivalently, the surface area of a regular octahedron with unit volume. Among Platonic solids, surface indices decrease with increasing number of faces: this one, 6.0 (cube = hexahedron), A232811 (octahedron), A232810 (dodecahedron), and A232809 (icosahedron).
%H Stanislav Sykora, <a href="/A232812/b232812.txt">Table of n, a(n) for n = 1..1000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Platonic_solid">Platonic solid</a>.
%H <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a>
%F Equals 2*sqrt(3)*3^(2/3).
%F Equals A002194/A020829^(2/3).
%e 7.20562173105601636005279232409725707779044450935589335...
%t RealDigits[2*Sqrt[3]*3^(2/3), 10, 120][[1]] (* _Amiram Eldar_, May 25 2023 *)
%o (PARI) sqrtn(139968,6) \\ _Charles R Greathouse IV_, Apr 25 2016
%Y Cf. A002194, A020829, A232808 (surface index of a sphere), A232809, A232810, A232811.
%K nonn,cons,easy
%O 1,1
%A _Stanislav Sykora_, Dec 01 2013
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