Edge-illumination tomography is a modality for performing x-ray phase-contrast imaging in 3D, based on structuring the primary beam into an array of beamlets and employing a dedicated incoherent sensing mechanism. In this article, we provide a theoretical framework for the spatial resolution of this method, based on the concept of the bowtie-shaped essential support of the Radon transform in frequency space, which is well known in conventional tomography. The additional complexity caused by the use of beamlets is added to the model, and its validity is confirmed by means of simulated and experimental results. In essence, we show that the precise location of non-negligible entries in the two-dimensional frequency spectrum of an edge-illumination sinogram can be predicted by only two parameters, the beamlet width and the sample thickness. This enables the derivation of sampling schemes tailored to avoid aliasing, thus maximizing spatial resolution.