In the geometry of crystal nets, one can treat edges as line segments. For example, in a crystal net, it is presumed that edges do not “collide” in the sense that when treating them as line segments, they do not intersect. Several polyhedral constructions can be derived from crystal nets. For example, a vertex figure can be obtained by subdividing each edge (treated as a line segment) by the insertion of subdividing points, and then the vertex figure of a given vertex is the convex hull of the adjacent subdividing points (i.e., the convex polyhedron whose vertices are the adjacent subdividing points).
Another polyhedral construction is to determine the neighborhood of a vertex in the crystal net. One application is to define an energy function as a (possibly weighted) sum of squares of distances from vertices to their neighbors, and with respect to this energy function, the net is in equilibrium (with respect to this energy function) if each vertex is positioned at the centroid of its neighborhood, this is the basis of the crystal net identification program SYSTRE. (mathematicians 
 use the term ``harmonic realiaztions" instead of ``crystal nets in equilibrium positions" because the positions are characterized by the discrete Laplace equation; they also introduced the notion of standard realizations which are special harmonic realizations characterized by a certain minimal principle as well;see ). Some crystal nets are isomorphic to crystal nets in equilibrium positions, and since an equilibrium position is a normal form, the crystal net isomorphism problem (i.e., the query whether two given crystal nets are isomorphic as graphs; not to be confused with crystal isomorphism) is readily computed even though, as a subsumption of the graph isomorphism problem, it is apparently computationally difficult in general.