CASSCF and CASPT2 methods were used to study the photochemistry of tricyclo[3.3.0.0(2,6)]octa-3,7-diene (TOD). The analysis of different S1 reaction paths as well as the topology of the S1/S0 intersection space allows us to establish two novel properties associated with the photochemical behavior of this compound: (i) simple low-lying intersection space domains can mediate different photoproducts, and (ii) TOD photochemistry is probably mediated by two disconnected intersection space domains, related to the formation of cyclooctatetraene and semibulvalene in different time-scales. It is shown that these domains are chemically distinct since the first, leading to COT, mediates barrierless pericyclic reactions while the second, leading to SBV, is accessed through the formation of an excited-state biradical intermediate. To the best of our knowledge, in the domain of single molecule photochemistry, TOD represents the first example where a different chemical role of distinct low-lying intersection spaces has been computationally documented. The observed photoproducts can be rationalized in terms of branching space diagrams, constructed by determining the branching space (derivative coupling and gradient difference vectors) for each conical intersection involved in the photochemical process.