Doubly periodic monopoles (aka Monowalls) are good sources of interesting hyperkahler manifolds. For example, they deliver complete hyperkahler metrics on elliptically fibered surfaces. We classify the resulting moduli spaces and study their compactification in terms of exploded geometry. Analyzing monopole dynamics, we find the asymptotic Kahler potential on the moduli spaces and observe that it is given in terms of the volume of an associated plane arrangement in the Euclidean three-space.