The feasibilities of Fujita's unit-subduced-cycle-index (USCI) approach, Fujita's proligand method, and Fujita's stereoisogram approach have been demonstrated by applying them to cubane derivatives as probes. They provide us with a new set of theoretical foundations for comprehensive investigation of geometric and stereoisomeric features of stereochemistry. The new set of theoretical foundations is based on mathematical formulations so as to explore mathematical stereochemistry as a new interdisciplinary field of stereochemistry.