The multidimensional conformational potential energy hypersurface (PEHS) of cyclic Gly-Gly-Gly (1,4,7-triazonane-2,5,8-trione) was comprehensively investigated at the Hartree-Fock (RHF/6-31G(d)) level of theory. The equilibrium structures, their relative stability, and the transition state (TS) structures involved in the conformational interconversion pathways were analyzed. aug-cc-pVTZ//B3LYP/6-311++G** single point calculations predict a trans-cis-cis conformation as the energetically preferred form for this compound. However, all of the levels of theory employed here predicted that two forms, a trans-cis-cis and a cis-cis-cis (crown), of conformers contribute significantly to the equilibrium mixture at room temperature. The conformational interconversion between the global minimum and the symmetric cis-cis-cis crown form requires 12.49 kcal/mol at the RHF 6-31G(d) level of theory, whereas the conformational interconversion between the cis-cis-cis crown and cis-cis-cis boat form requires 18.70 kcal/mol. An exploratory topological analysis of the PEHS was also carried out. Our results allow us to form a concise idea about the internal intricacies of the PEHSs of these cyclic tripeptides, describing the conformations as well as the conformational interconversion processes in these hypersurfaces.