Research on cognitive sex differences reveals a male advantage in certain tasks of spatial ability but the extent, development, and universality of this advantage merit further exploration. We tested adults and 6-10-year-old children in Boston and in a set of Munduruku villages in the Brazilian Amazon on a new measure of sensitivity to a variety of geometrical relationships in visual arrays of points, lines, and figures (Dehaene, Izard, Pica & Spelke, in press; after Franco & Sperry, 1977). On each of 45 trials, participants saw five arrays depicting the same geometrical property in otherwise variable figures, and a sixth, randomly placed array that lacked the target property. Their task was to detect the outlying figure. Overall, performance did not differ by sex in any sample. U.S. adult males and females showed equal overall performance, although two items testing chirality showed a marginal male advantage, consistent with the findings of many studies of "mental rotation" (Hyde, 2005). U.S. children also showed no overall sex difference, but males performed reliably better on one item testing chirality, whereas females performed reliably better on two items testing symmetry and polygons. In the Munduruku sample, there was again no overall sex difference, but males performed slightly better on symmetry items. Most important, item by item performance of the males and females was highly correlated in both U.S. and Munduruku samples and in both children and adults. These correlations provide evidence for strong invariance in core sensitivity to geometry across age, culture, and gender.