  Box graphs, or equivalently Coulomb phases of three-dimensional N=2
supersymmetric gauge theories with matter, give a succinct, comprehensive and
elegant characterization of crepant resolutions of singular elliptically
fibered varieties. Furthermore, the box graphs predict that the phases are
organized in terms of a network of flop transitions. The geometric construction
of the resolutions associated to the phases is, however, a difficult problem.
Here, we identify a correspondence between box graphs for the gauge algebras
su(2k+1) with resolutions obtained using toric tops and generalizations
thereof. Moreover, flop transitions between different such resolutions agree
with those predicted by the box graphs. Our results thereby provide explicit
realizations of the box graph resolutions.
