 This homogeneity remains the case for the free abelian group on 2 generators, whose vertices are still of degree 4. However the additional identifications turns it from a tree (a graph with no cycles) to a grid whose vertices are the lattice points of the plane. That is, the free abelian group on 2 generators is \(Z^2\), and on \(n\) generators \(Z^n\). The edges are the line segments joining adjacent lattice points.