We have shown how a combination of x-ray tomography, image analysis-type techniques, and spherical harmonic analysis can give a complete 3-D mathematical characterization of an aggregate particle. Detailed information about the particle can be obtained from this description. The derived mathematical form of the real particle also allows incorporation of the particle into various algorithms, allowing real particle shape to be used in models that before only were able to use simple shapes like spheres and ellipsoids. Databases of 3-D aggregate shape can be constructed, characterizing various aggregate sources. The rheology of a suspension of real particles can now be simulated with good accuracy, which should result in a useful computational tool for concrete.