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Show that there exists a set of circles [ILL 1974]

Source:

January 2, 2011
geometry3D geometryspheregeometry unsolved

Problem Statement

Show that there exists a set SS of 1515 distinct circles on the surface of a sphere, all having the same radius and such that 55 touch exactly 55 others, 55 touch exactly 44 others, and 55 touch exactly 33 others.
[General Problem: http://www.artofproblemsolving.com/Forum/viewtopic.php?f=46&t=384764]
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