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The structure of the naturally occurring, iron-rich mineral Ca_1.08(6)Mg_0.24(2)Fe_0.64(4)Mn_0.04(1)(CO₃)₂ ankerite was studied in a joint experimental and computational study. Synchrotron X-ray powder diffraction measurements up to 20 GPa were complemented by density functional theory calculations. The rhombohedral ankerite structure is stable under compression up to 12 GPa. A third-order Birch–Murnaghan equation of state yields <i>V</i>₀ = 328.2(3) ų, bulk modulus <i>B</i>₀ = 89(4) GPa, and its first-pressure derivative <i>B</i>’₀ = 5.3(8)—values which are in good agreement with those obtained in our calculations for an ideal CaFe(CO₃)₂ ankerite composition. At 12 GPa, the iron-rich ankerite structure undergoes a reversible phase transition that could be a consequence of increasingly non-hydrostatic conditions above 10 GPa. The high-pressure phase could not be characterized. DFT calculations were used to explore the relative stability of several potential high-pressure phases (dolomite-II-, dolomite-III- and dolomite-V-type structures), and suggest that the dolomite-V phase is the thermodynamically stable phase above 5 GPa. A novel high-pressure polymorph more stable than the dolomite-III-type phase for ideal CaFe(CO₃)₂ ankerite was also proposed. This high-pressure phase consists of Fe and Ca atoms in sevenfold and ninefold coordination, respectively, while carbonate groups remain in a trigonal planar configuration. This phase could be a candidate structure for dense carbonates in other compositional systems.