Abstract
Given the complete set R of rank orders derived from some configuration of n stimulus points in r dimensions in accordance with the unfolding model, a stimulus configuration which generates just these orders will be described as a solution for R. The space is assumed to be Euclidean. Necessary and sufficient conditions are determined for a nondegenerate configuration to be a solution for R. The geometrical conditions which are necessary and sufficient to determine the subset of pairs of opposite orders are also identified and constitute the constraint system for the ordinal vector model.