This manuscript outlines a methodology and algorithm for the design of shell-lattice structures based on dual regular and semi-regular planar shapes. It introduces a 2-manifold, parametric freeform shell type of tiling to tessellate the domain of any given bivariate deformation map. The tessellated domain is functionally composed into the deformation map to obtain freeform shell-lattice structures in 3-space. Given any primal regular or semi-regular pattern, intrinsic controls over the thickened parameters of the dual graph are provided, results in a variety of tilings that differs in both physical properties and aesthetic appearance. Curve, surfaces, and trivariate tilings are offered, allowing analysis, optimization and fabrication of the shell-lattice results. This work concludes with several results from the implementation of the algorithms, including of 3D printed parts.