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 A239798 Decimal expansion of the midsphere radius in a regular dodecahedron with unit edges. 7

%I

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

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

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

%N Decimal expansion of the midsphere radius in a regular dodecahedron with unit edges.

%C In a regular polyhedron, the midsphere is tangent to all edges.

%C Apart from leading digits the same as A019863 and A019827. - _R. J. Mathar_, Mar 30 2014

%H Stanislav Sykora, <a href="/A239798/b239798.txt">Table of n, a(n) for n = 1..2000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Platonic solid">Platonic solid</a>

%F Equals phi^2/2, phi being the golden ratio (A001622).

%F Also (3+sqrt(5))/4.

%e 1.30901699437494742410229341718281905886015458990288143106772431135263...

%p Digits:=100: evalf((3+sqrt(5))/4); # _Wesley Ivan Hurt_, Mar 27 2014

%t RealDigits[GoldenRatio^2/2,10,105][[1]] (* _Vaclav Kotesovec_, Mar 27 2014 *)

%o (PARI) (3+sqrt(5))/4

%Y Cf. A001622,

%Y Midsphere radii in Platonic solids:

%Y A020765 (tetrahedron),

%Y A020761 (octahedron),

%Y A010503 (cube),

%Y A019863 (icosahedron).

%K nonn,cons,easy

%O 1,2

%A _Stanislav Sykora_, Mar 27 2014

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Last modified April 5 05:06 EDT 2020. Contains 333238 sequences. (Running on oeis4.)