For the construction of the bicyclo[2.2.2]octane skeleton, 2,2-dimethyl-3a,7a-dihydro-1,3-benzodioxole was reacted with vinylene carbonate to give two isomeric cycloadditon products having the bicyclo[2.2.2]octane skeleton. Hydrolysis of the ketal ring and the opening of the carbonate functionality, followed by hydroxylation of the remaining double bond resulted in the formation of a symmetrical hexol. Epoxidation of the double bond in the cycloaddition products and the subsequent ring-opening reactions produce two additional hexol derivatives. One of the synthesized molecules exhibited enzyme-specific inhibition against alpha-glycosidase.