Plant leaves typically have two layers of photosynthetic tissue, the palisade and spongy mesophyll. While palisade mesophyll consists of tightly packed columnar cells, spongy mesophyll is often treated as a random assemblage of irregularly shaped cells. Here, we characterized the three-dimensional structure of the spongy mesophyll in laminar leaves with reticulate venation in 40 species representing 30 genera. In most species, lobed cells gave rise to an ordered structure with the topological and functional properties of a honeycomb. A subset of species with small cells, high cell packing densities, and closely spaced veins had an irregular morphology associated with high surface-area-to-volume ratios and maximum photosynthetic rates. Morphological variation followed allometric scaling laws with constraints imposed by cell and genome size. Our study suggests that simple biophysical principles may govern the patterning of the spongy mesophyll, providing a platform for spatially explicit analyses of leaf development, physiology, and biomechanics.