The crystal structure of the first oligomeric cobalt dioxolene complex, Co3(3,5-DBSQ)2((t)BuCOO)4(NEt3)2, 1, where DBSQ is 3,5-di-tert-butyl-semiquinonate, has been studied at various temperatures between 20 and 200 K. Despite cobalt-dioxolene complexes being generally known for their extensive ability to exhibit valence tautomerism (VT), we show here that the molecular geometry of compound 1 is essentially unchanged over the full temperature range, indicating the complete absence of electron transfer between ligand and metal. Magnetic susceptibility measurements clearly support the lack of VT between 8 and 300 K. The crystal structure is also determined at elevated pressures in the range from 0 to 2.5 GPa. The response of the crystal structure is surprisingly dependent on the dynamics of pressurisation: following rapid pressurization to 2 GPa, a structural phase transition occurs; yet, this is absent when the pressure is increased incrementally to 2.6 GPa. In the new high pressure phase, Z' is 2 and one of the two molecules displays changes in the coordination of one bridging carboxylate from μ2:κO:κO' to μ2:κ(2)O,O':κO', while the other molecule remains unchanged. Despite the significant changes to the molecular connectivity, analysis of the crystal structures shows that the phase transition leaves the spin and oxidation states of the molecules unaltered. Intermolecular interactions in the high pressure crystal structures have been analysed using Hirshfeld surfaces but they cannot explain the origin of the phase transition. The lack of VT in this first oligomeric Co-dioxolene complex is speculated to be due to the coordination geometry of the terminal Co-atoms, which are trigonal bipyramidally coordinated, different from the more common octahedral coordination. The energy that is gained by a hs-to-ls change in Oh is equal to Δ, while in the case of the trigonal bipyramidal (C3v), the energy gain is equal to the splitting between d(z(2)) and degenerate d(x(2) - y(2))/d(xy), which is significantly less.