This chapter presents a conceptually simple method for constructing flagstone tessellations, which has surprising connections to the shrink-rotate algorithm and James Clerk Maxwell's reciprocal figure. The shrink-rotate algorithm works for a wide range of tilings—all tilings composed of regular polygons, among others. An interesting property of flagstone tessellations is that the completed tessellation is a reduced-size copy of the original tiling. This is in contrast to ordinary shrink-rotate tilings, for which the tiles are offset relative to one another. The primal-dual tessellations illustrate a generalizable concept: take an existing mathematical tiling and then transform it mathematically to realize an origami tessellation in which folds recreate some aspect of the original tiling. The dual and interior dual graphs are topological concepts: they exist without actually having to be drawn on a surface. However, it is easily shown that both the dual graph and interior dual graph are planar graphs—capable of being drawn on a plane or sphere with no crossings.