The “M” in digital elevation models (DEM) stands for model, which literally means “a schematic description of a system, theory, or phenomenon that accounts for its known or inferred properties and may be used for further study of its characteristics.” A DEM fulfills the requirement of “a schematic description” of terrain. However, how to make it account for the “known or inferred properties” warrants further scrutiny. This article outlines three properties of terrain and examines their four implications to DEM generation. The three properties are as follows: (1) each terrain point has a single, fixed elevation; (2) terrain points have an order and sequence that is determined by their elevations; and (3) terrain has skeletons. The four implications to DEM generation methods are as follows: (1) a method must be a bijection; (2) a method must be an isomorphism in order to preserve elevation sequence; (3) a method must guarantee that the vertical error at any point, not just checkpoints, is acceptable in orde...