We investigate the three-dimensional (3-D) stratigraphic structure of the south polar layered deposits (SPLD) on Mars. Prominent bench-forming layers exposed on SPLD scarps were observed and mapped in three dimensions using high-resolution topographic and imaging data sets. Using the 3-D location of exposures of one of these strata, we can accurately describe the shape of that layer using simple mathematical functions. Analysis of these functions and the surface topography can be used to reliably predict where on other scarps this layer is exposed. In general this bench-forming layer (and its surrounding strata) is not flat and is well approximated as a parabolic dome near the center of the SPLD. Its curvature indicates that when deposited it was draped over a topographic dome similar in size to that of the present day. The scarps in which this layer is exposed must have formed subsequently and have not been significantly modified by flow processes. The basement topography exercises some control over the shape of the interior strata in extreme cases. Our successful layer-fitting technique illustrates the regional uniformity in layer formation and the lack of major internal defects (such as faulting) within the SPLD. We have mapped exposures of what appear to be this layer in scarps farther from the center of the deposits. The position of these exposures can be used to modify the modeled parabolic shape at the periphery of the SPLD. These peripheral elevations provide constraints on the role of flow in the overall shaping of the SPLD.