In the middle of the 10th century, four innovative ribbed vaults were built in the extension of the mosque of Córdoba. Their pattern of crossed-arch vaults together with the early and systematic use of ovals for the ribs, make them a unique case to research. A survey using total station measurements, and a study of the constructive evidence, have led to interesting conclusions about their geometry and construction. This paper discusses the geometry of the ribs, as well as the construction process of these vaults.