Karbandi is a ribbed masonry vault form based on a stellar harmonic geometry in Iranian historical architecture. The present article aims to unfold the geometric characteristics of Karbandi and use them as the basis of parametric design algorithms. This work presents a new method for automated geometric design of large-size Karbandi vaults. For this purpose, the configuration process of three prominent large-size historical cases is analyzed and their geometrical and mathematical principles are extracted and generalized. Accordingly, two parametric algorithms are formulated to design regular and semiregular large-size Karbandi vaults that are then implemented in the Grasshopper visual programming language. Results show that a 3D modeling procedure has been developed by considering all types of large-size Karbandi vaults, which can generate their different models by changing the inputs. In the models, all geometric parameters of the Karbandi, including the shape of the base plan, the intricacy degree of elements, and the number of arches and proportions of their cross section, can be controlled and modified. The output geometries are entirely composed of solid elements, so they can be applied for metaheuristic structural and multidisciplinary optimizations and 3D numerical finite-element analysis.