We have studied the relative stability and atomic structures of five $C_{20}X_2$ regioisomers obtained as diadducts of a $C_{20}$ cage (X = H, F, Cl, Br, and OH). All the regioisomers are geometric isomers, i.e., they differ in their spatial arrangement. Full-geometry optimizations of the regioisomers have been performed using the hybrid density-functional (B3LYP/6-31G(d, p)) method. Our results suggest that the cis-1 regioisomer (the 1,2-diadduct) is the most stable and that the second most stable is the trans-2 (1,13-diadduct) regioisomer, implying that the long-range interaction between the two adducts and the resonance effect are more pronounced than the diadduct-induced strain in the $C_{20}$ cage. The HOMO and LUMO characteristics of each regioisomer with the same symmetry of structural regioisomers except $C_{20}(OH)_2$ are topologically same. This suggests that by using an entirely different set of characteristic chemical reactions for each regioisomer, we can distinguish between the five regioisomers for each $C_{20}$ diadduct derivative.