Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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