As  describes, the vertices of the Laves graph can be defined by selecting one out of every eight points in the three-dimensional integer lattice, and forming their nearest neighbor graph. Specifically, one chooses the points
and all the other points formed by adding multiples of four to these coordinates. The edges of the Laves graph connect pairs of points whose Euclidean distance from each other is the square root of two, , as the points of each pair differ by one unit in two coordinates, and are the same in the third coordinate. The edges meet at 120° angles at each vertex, in a flat plane. All pairs of vertices that are non-adjacent are farther apart, at a distance of at least  from each other. The edges of the resulting geometric graph are diagonals of a subset of the faces of the regular skew polyhedron with six square faces per vertex, so the Laves graph is embedded in this skew polyhedron.
It is possible to choose a larger set of one out of every four points of the integer lattice, so that the graph of distance- pairs of this larger set forms two mirror-image copies of the Laves graph, disconnected from each other, with all other pairs of points farther than  apart.