Size reduction of a point cloud or triangulated mesh is an intrinsic part of a three-dimensional (3D) documentation process, reducing the data volume and filtering out erroneous and redundant data obtained during acquisition. Additional reduction has an effect on the geometric accuracy of 3D data compared to the tangible object, and for 3D objects utilized in various cultural heritage applications, the small geometric properties of an object are equally as important as the large ones. In this paper, we investigate several simplification algorithms and various geometric features’ relevance to geometric accuracy during the reduction of a 3D object’s data size, and whether any of these features have a particular relation to the results of an algorithmic approach. Different simplification algorithms have been applied to several primitive geometric shapes at several reduction stages, and measured values for geometric features and accuracy have been tracked across every stage. We then compute and analyze the correlation between these values to see the effect each algorithm has on different geometries, and whether some of them are better suited for a simplification process based on the geometric features of a 3D object.