It is well known that there exists a triangulated packing in the plane with equal sized disks - the hexagonal packing. Assuming the largest disks have unit radii, we can interpret the radii of the smallest disks, q, as a measure of how uniform a packing is. The hexagonal packing is the most uniform triangulated packing. What is the second most uniform triangulated packing? Fejes Toth proposed a packing with q~0.638 in his book Regular Figures published in 1965. Fernique improved it with another packing with q~0.651 in 2019. We will discuss the connection between this problem and rigidity theory.