The strong dependence of shear and flow behavior of granular materials on particle morphology is a well known fact. Quantification of three dimensional shapes yields a useful tool to investigate the correlation between particle morphology and shear behavior. Particle regeneration of realistic shapes in a discrete element program is also critical if a good understanding of micromechanics of granular media is required. This paper describes three-dimensional shape descriptors that can be used to describe morphology of particle aggregates as well as particle reconstruction techniques utilizing tomographic principles. The paper demonstrates that a single set of numbers representing a composite three-dimensional shape can be used to characterize all the varying three-dimensional shapes of similar particles in an aggregate mix. The composite shape is obtained by subdividing the problem into a judicious combination of simple techniques - two-dimensional shape description using Fourier and/or invariant moment descriptors, feature extraction using principal component analysis, statistical modeling and projective reconstruction. Results demonstrating the consistency, separability and uniqueness of the three-dimensional shape descriptor algorithms are presented. The paper also attempts to synthesize composite 3-D granular particles from statistically obtained 3-D shape descriptors of the particles in a granular particle mixture using Algebraic Reconstruction Technique. The paper also attempts to validate the premise that multiple projective representations of multiple particles could be used to synthesize a composite 3-D particle that represents the entire mixture in terms of its 3-D shape descriptors. Validation of the premise is attempted by investigating the statistical similarity between the regenerated particle using multiple projective representations of multiple particles and multiple projective representations of a single particle using optical and X-ray tomography techniques. This research work proves useful for generating realistic shapes for discrete element applications.