The interest in titanium dioxide (TiO2) phases is growing due to the number of applications in cosmetics, food industry andphotocatalysis, an increase that is driven by its exceptional properties when engineered at the nanoscale like in the form ofnanoparticles. Our goal is to discovered previously unknown low-density phases of TiO2, with potential for applications invarious fields. We then use well-known TiO2 clusters as fundamental building blocks to be self-assembled into unique structuresto study their distinct characteristics. Density functional calculations are emplyed to relax the structures and identify the moststable TiO2 structures within an energy range of 0.1 eV per atom from the rutile and anatase phases, which are confirmed,validating our methodology. Going beyond conventional phases, we found two-dimensional TiO2 structures, previously exploredin separate studies, and showing typical structures of transition metal dichalcogenide layers, that forge a bridge betweendifferent TiO2 structures. It is noteworthy that our investigation uncovered an entirely novel class of TiO2 structures featuringhexagonal cages like beehive channels, opening novel phases with huge potential. These discovered low-density phases areinteresting, particularly the hexagonal cage structures with remarkable large gaps, because they introduce other dimensions foruncharted applications in the ever-growing TiO2 landscape.