Experimental results from an investigation of the assembly of two-dimensional granular piles are presented. Three different particle shapes were used in the investigation of the evolution of piles towards isostatic and isotropic granular assemblies. Good agreement is found with previous experimental results for all particle shapes. We attempt to classify the divergence of a characteristic length-scale of the system as a power law and provide an estimate of the critical exponent. We find that the results are independent of particle shapes and speculate this may be a general feature of two-dimensional convex particles.