  Piecewise Euclidean structures (identified solid Euclidean polyhedra) on
topological 3-dimensional manifolds and pseudo-manifolds are constructed so
that they admit pseudo-foliations, a generalized type of foliation. The
construction of non-manifold point neighborhoods is done to preserve as much of
the geometric, and vector space, structure of Euclidean space as possible. This
enables structures, such as foliations and calibrations, to generalize over to
pseudo-manifolds. The main result is that the cone of any compact topological
surfaces can be given a piecewise flat metric structure that admits a
pseudo-foliation by minimal surfaces. In some situations orientation reversing
holonomy is an obstruction and in others it is just the opposite, a sufficient
condition. Also foliations by minimal surfaces can extend across connect sum
operations.
