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%I #27 Oct 11 2019 03:03:12
%S 1,4,2,5,2,3,2,9,2,1,5,0,1,1,3,5,6,3,9,3,9,0,4,6,2,1,8,8,8,5,1,1,0,8,
%T 3,2,8,6,2,0,6,6,0,8,5,8,0,9,7,7,6,1,0,8,8,9,3,7,1,5,4,8,7,4,7,8,3,1,
%U 8,7,0,0,1,5,5,5,8,5,3,5,4,3,1,6,2,1,6,2,1,9,4,7,5,4,5,7,5,7,1,5,1,6,4,6,5,5,8,4,8,7,8
%N Johannes Kepler's polyhedron circumscribing constant.
%C The finite solid analogy to the plane polygon circumscribing constant (A051762).
%C The five Platonic solids are the tetrahedron, the hexahedron or cube, the octahedron, the dodecahedron and the icosahedron.
%C The geometric interpretation is as follows. Begin with a unit sphere. Circumscribe a tetrahedron and then circumscribe a sphere. Circumscribe a cube and then circumscribe a sphere. Circumscribe an octahedron and then circumscribe a sphere. Circumscribe a dodecahedron and then a sphere. Circumscribe an icosahedron and then a sphere. The constant is the radius of this last sphere. In actuality, it makes no difference the order of the five solids.
%H Rüdiger Appel, <a href="http://www.3quarks.com/en/PlatonicSolids/index.html">3Quarks: Platonic Solids</a> (September 2010).
%H David A. Fontaine, <a href="http://davidf.faricy.net/polyhedra/platonic_solids.html">The Five Platonic Solids.</a>
%H George W. Hart, Virtual Polyhedra, 1998, <a href="http://www.georgehart.com/virtual-polyhedra/kepler.html">Johannes Kepler's Polyhedra.</a>
%H Omar E. Pol, <a href="http://gaussianos.com/circunferencias-concentricas-y-poligonos-regulares-inscritos">Circunferencias concéntricas y polígonos regulares inscritos</a>, gaussianos, Nov 17 2007, 13:17
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Platonic_solid">Platonic Solids.</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Johannes_Kepler">Johannes Kepler.</a>
%H Wikipedia, <a href="http://upload.wikimedia.org/wikipedia/commons/1/19/Kepler-solar-system-1.png">Kepler solar system.</a>
%F = 9*(15 - 6*sqrt(5)).
%e 14.25232921501135639390462188851108328620660858097761088937154874783...
%t RealDigits[ 9(15 - 6 * Sqrt[5]), 10, 111][[1]]
%Y Cf. A051762.
%K cons,nonn
%O 2,2
%A _William H. Richardson_ and _Robert G. Wilson v_, Feb 01 2013
%E Offset corrected by _Rick L. Shepherd_, Dec 31 2013
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