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The Leiter International Performance Scale-Revised (Leiter-R) is a standardized cognitive test that seeks to "provide a nonverbal measure of general intelligence by sampling a wide variety of functions from memory to nonverbal reasoning." Understanding the computational building blocks of nonverbal cognition, as measured by the Leiter-R, is an important step towards understanding human nonverbal cognition, especially with respect to typical and atypical trajectories of child development. One subtest of the Leiter-R, Form Completion, involves synthesizing and localizing a visual figure from its constituent slices. Form Completion poses an interesting nonverbal problem that seems to combine several aspects of visual memory, mental rotation, and visual search. We describe a new computational cognitive model that addresses Form Completion using a novel, mental-rotation-friendly image representation that we call the Polar Augmented Resolution (PolAR) Picture, which enables high-fidelity mental rotation operations. We present preliminary results using actual Leiter-R test items and discuss directions for future work.