Photonic lanterns rely on a close packed arrangement of single mode fibers, which are tapered and fused into one multi-mode core. Topologically optimal circle packing arrangements have been well studied. Using this, we fabricate PLs with 19 and 37 SMFs showing tightly packed, ordered arrangements with packing densities of 95 % and 99 % of theoretically achievable values, with mean adjacent core separations of 1.03 and 1.08 fiber diameters, respectively. We demonstrate that topological circle packing data is a good predictor for optimal PL parameters.