A symmetry of a Euclidean graph is an isometry of the underlying Euclidean space whose restriction to the graph is an automorphism; the symmetry group of the Euclidean graph is the group of its symmetries. A Euclidean graph in three-dimensional Euclidean space is periodic if there exist three linearly independent translations whose restrictions to the net are symmetries of the net. Often (and always, if one is dealing with a crystal net), the periodic net has finitely many orbits, and is thus uniformly discrete in that there exists a minimum distance between any two vertices.
The result is a three-dimensional periodic graph as a geometric object.
The resulting crystal net will induce a lattice of vectors so that given three vectors that generate the lattice, those three vectors will bound a unit cell, i.e. a parallelepiped which, placed anywhere in space, will enclose a fragment of the net that repeats in the directions of the three axes.