Abstarct We introduce Hypercat, a large set of 2-d AGN torus images computed with the state-of-the-art clumpy radiative transfer code Clumpy. The images are provided as a 9-dimensional hypercube, in addition to a smaller hypercube of corresponding projected dust distribution maps. Hypercat also comprises a software suite for easy use of the hypercubes, quantification of image morphology, and simulation of synthetic observations with single-dish telescopes, interferometers, and Integral Field Units. We apply Hypercat to NGC 1068 and find that it can be spatially resolved in Near- and Mid-IR, for the first time with single-dish apertures, on the upcoming generation of 25-40m class telescopes. We also find that clumpy AGN torus models within a range of the parameter space can explain on scales of several parsec the recently reported polar elongation of MIR emission in several sources, while not upending basic assumptions about AGN unification.