Following the discovery of a series of geometric designs on the floor of the Biblioteca Laurenziana in Florence we analyse the "Medici panel", which consists of a circular rosette containing a set of inscribed elliptical disks, with a view to regenerating the pattern. The geometry is shown to be surprisingly complex. We were able to determine a numerical solution for synthesising the pattern. Alternatively we found analytic solutions for simpler patterns such as inscribed circles or polygonal rosettes.