  By applying a standard solution generating technique, we transform an
arbitrary vacuum Mixmaster solution on $S^3 \times {\bf R}$ to a new solution
which is spatially inhomogeneous. We thereby obtain a family of exact,
spatially inhomogeneous, vacuum spacetimes which exhibit Belinskii,
Khalatnikov, and Lifshitz (BKL) oscillatory behavior. The solutions are
constructed explicitly by performing the transformations on numerically
generated, homogeneous Mixmaster solutions. Their behavior is found to be
qualitatively like that seen in previous numerical simulations of generic U(1)
symmetric cosmological spacetimes on $T^3 \times {\bf R}$.
