Euclidean Distance Matrix Analysis (EDMA) is widely held as the most important coordinate-free method by which to analyze landmarks. It has been used extensively in the field of medical anthropometry and has already produced many useful results. Unfortunately this method renders little information regarding the surface on which these points are located and accordingly is inadequate for the 3D analysis of surface anatomy. Here we shall present a new inverse surface flatness metric, the ratio between the Geodesic and the Euclidean inter-landmark distances. Because this metric also only reflects one aspect of three-dimensional shape, i.e. surface flatness, we have combined it with the Euclidean distance to investigate 3D facial change. The goal of this investigation is to be able to analyze three-dimensional facial change in terms of bilateral symmetry as encoded both by surface flatness and by geometric configuration. Our initial study, based on 25 models of surgically managed children (unilateral cleft lip repair) and 40 models of control children at the age of 2 years, indicates that the faces of the surgically managed group were found to be significantly less symmetric than those of the control group in terms of surface flatness, geometric configuration and overall symmetry.