Our legal regimes are crafted in a way that asserts control over a certain physical three-dimensional space. Some property regimes assert dominion over a vertical three-dimensional column, such as ownership of land that includes certain resources that are vertically related to it above and below the ground. Other property regimes, however, control resources on the horizontal axis. For example, legal control over a footpath exerts a kind of horizontal dominion over the space of and around the footpath. This article offers a conceptual framework for unpacking the spatial geometry of our property regimes and underscores its significance for policy and institutional design. It shows, importantly, that the compatibility between the space over which a regime holds control, and the space that is occupied by a particular resource, has profound implications. A misalignment between the two – for example, when a vertical regime is applied to a horizontal resource – implicates how well the regime functions. After laying out the conceptual framework, the article illustrates its application to a contemporary problem of extracting wind energy.