A fundamental question in human cognition is how people reason about space. We use a computational model to explore cross-cultural commonalities and differences in spatial cognition. Our model is based upon two hypotheses: (1) the structure-mapping model of analogy can explain the visual comparisons used in spatial reasoning; and (2) qualitative, structural representations are computed by people's visual systems and used in these comparisons. We apply our model to a visual "oddity task," in which individuals are shown an array of two-dimensional images and asked to the pick the one that does not belong. This task was previously used to evaluate understanding of geometric concepts in two disparate populations: North Americans, and the Munduruku, a South American indigenous group. Our model automatically generates representations of each hand-segmented image and compares them to solve the task. The model achieves human-level performance on this task, and problems that are hard for the model are also difficult for people in both cultures. Furthermore, ablation studies on the model suggest explanations for cross-cultural differences in terms of differences in spatial representations. (Contains 7 tables and 3 figures.)