  For a finite multigraph G, let \Lambda(G) denote the lattice of integer flows
of G -- this is a finitely generated free abelian group with an integer-valued
positive definite bilinear form. Bacher, de la Harpe, and Nagnibeda show that
if G and H are 2-isomorphic graphs then \Lambda(G) and \Lambda(H) are
isometric, and remark that they were unable to find a pair of nonisomorphic
3-connected graphs for which the corresponding lattices are isometric. We
explain this by examining the lattice \Lambda(M) of integer flows of any
regular matroid M. Let M_\bullet be the minor of M obtained by contracting all
co-loops. We show that \Lambda(M) and \Lambda(N) are isometric if and only if
M_\bullet and N_\bullet are isomorphic.
