To gain more insights into the mechanistic details, two control experiments were performed (Scheme 6A). When BCB 1a or imidazolidine/hexahydropyrimidine 2a/3a was subjected to the standard reaction In summary, we have developed a modular and efficient approach for the formal (n+3) (n = 5,6) cycloaddition of BCBs with imidazolidines/hexahydropyrimidines under B(C6F5)3 catalysis, offering two series of synthetically challenging medium-bridged rings, 2,5-diazabicyclo[5.1.1]nonanes and 2,6diazabicyclo[6.1.1]decanes. The reaction proceeds under mild reaction conditions and tolerates a broad range of BCBs and imidazolidines/hexahydropyrimidines. The potential synthetic utility of the reaction has also been highlighted by a scale-up experiment and various synthetic transformations of products. As we know, this methodology represents the first Lewis acid catalyzed high order (n+3) (n > 3) cycloaddition of BCBs. Given the novel reactivity of this transformation and the high demand for conformationally restricted bicyclic molecules in drug design and development, we envision that this methodology will have an impact in both synthetic and medicinal chemistry. Further studies will be reported in due course.