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Abstract Although many collisional orogens form after subduction of oceanic lithosphere between two continents, some orogens result from strain localization within a continent via inversion of structures inherited from continental rifting. Intracontinental rift-inversion orogens exhibit a range of structural styles, but the underlying causes of such variability have not been extensively explored. We use numerical models of intracontinental rift inversion to investigate the impact of parameters including rift structure, rift duration, post-rift cooling, and convergence velocity on orogen structure. Our models reproduce the natural variability of rift-inversion orogens and can be categorized using three endmember styles: asymmetric underthrusting (AU), distributed thickening (DT), and localized polarity flip (PF). Inversion of narrow rifts tends to produce orogens with more localized deformation (styles AU and PF) than those resulting from wide rifts. However, multiple combinations of the parameters we investigated can produce the same structural style. Thus, our models indicate no unique relationship between orogenic structure and the conditions prior to and during inversion. Because the style of rift-inversion orogenesis is highly contingent upon the rift history prior to inversion, knowing the geologic history that preceded rift inversion is essential for translating orogenic structure into the processes that produced that structure.