  We construct a new (singular) cohomogeneity-three metric of G_2 holonomy. The
solution can be viewed as a triple intersection of smeared Taub-NUTs. The
metric comprises three non-compact radial-type coordinates, with the principal
orbits being a T^3 bundle over S^1. We consider an M-theory vacuum
(Minkowski)_4\times M_7 where M_7 is the G_2 manifold. Upon reduction on a
circle in the T^3, we obtain the intersection of a D6-brane, a Taub-NUT and a
6-brane with R-R 2-form flux. Reducing the solution instead on the base space
S^1, we obtain three intersecting 6-branes all carrying R-R 2-form flux. These
two configurations can be viewed as a classical flop in the type IIA string
theory. After reducing on the full principal orbits and the spatial
world-volume, we obtain a four-dimensional metric describing a lattice
universe, in which the three non-compact coordinates of the G_2 manifold are
identified with the spatial coordinates of our universe.
