In his famous work "Mysterium Cosmographicum" Kepler proposed a three dimensional model based on nested Platonic solids to explain the mainly two dimensional planetary orbital motions. Refer to the image below:
Question (of course this has nothing to do with Kepler's work) :
If the five platonic solids Tetrahedron, Cube, Octahedron, Dodecahedron and Icosahedron respectively (in that order) are packed inside spheres of optimum radius (i.e. most efficient packing) and if the length of side of Tetrahedron is 1 unit (which is the innermost platonic solid), find out the radius of outermost Sphere.
To avoid any misunderstanding, the configuration goes like this:
Firstly a Tetrahedron of unit side length is packed inside a sphere, which is inside a Cube packed inside a sphere, which is again inside a Octahedron packed inside a sphere, and so on.. . . this ends which a Icosahedron being packed inside a sphere.