We synthesized the inorganic anhydrous aluminum carbonates Al2[C2O5][CO3]2 and Al2[CO3]3 by reacting Al2O3 with CO2 at high pressures and temperatures and characterized them by Raman spectroscopy. Their structures were solved by X-ray diffraction. Al2[CO3]3 forms at around 24-28 GPa, while Al2[C2O5][CO3]2 forms above 38(3) GPa. The distinguishing feature of the new Al2[C2O5][CO3]2-structure type is the presence of pyrocarbonate [C2O5]2--groups, trigonal [CO3]2─groups, and octahedrally coordinated trivalent cations. Al2[CO3]3 has isolated [CO3]2--groups. Both Al-carbonates can be recovered under ambient conditions. Density functional theory calculations predict that CO2 will react with Fe2O3, Ti2O3, Ga2O3, In2O3, and MgSiO3 at high pressures to form compounds which are isostructural to Al2[C2O5][CO3]2. MgSi[C2O5][CO3]2 is predicted to be stable at pressures relative to abundant mantle minerals in the presence of CO2. This structure type allows the incorporation of four elements (Mg, Si, Fe, and Al) abundant in the Earth's mantle in octahedral coordination and provides an alternative phase with novel carbon speciation for carbon storage in the deep Earth.