In this paper we provide the following three examples of how the software system Mathematica can be used to reconstruct or model the three-dimensional shapes of folded surfaces. (1) First, we revisit the reconstruction of the central inclusion surface within a garnet porphyroblast that contains spiral-shaped inclusion trails. (2) Next, we revisit the reconstruction of five foliation surfaces that define oppositely concave folds within and surrounding a plagioclase porphyroblast. (3) For the main part of this paper we model superposed folds, and the many interference patterns that can be found in two-dimensional sections through these folds. Because this special issue is accompanied by a compact disk, we have included a series of reconstructions, models and animations to illustrate these three examples. Our reconstructions and models have, in some instances, provided important constraints on the interpretations of complex or controversial microstructures, and in all instances have provided useful teaching aids.