We report a complete characterization of the crystal structure between 400 and 80 K for RFe2O4 (R = Rm, Yb, and Lu) compounds using high resolution x-ray synchrotron powder diffraction. The three samples have a hexagonal structure (space group R3̄m) characterized by a sequence of double layers of mixed valence iron and oxygen atoms forming two-dimensional triangular layers separated by a single R-O layer along the c axis. This structure is stable down to 80 K for TmFe2O4 and YbFe2O4 though a sudden expansion in the c axis is observed at around 300 K coupled to a variation in the electrical properties. However, LuFe2O4 exhibits two structural transitions upon cooling. The splitting of some reflections and the occurrence of superstructure peaks below 320 K reveal a structural phase transition. The unit cell is monoclinic (space group C2/m), and there are four nonequivalent Fe sites with a maximum charge disproportionation of 0.5 e. The hexagonal to monoclinic transition is characterized by a sudden expansion of the c axis on cooling, and it seems to be driven by the condensation of Y2 modes. At lower temperatures (∼170 K) additional splitting of several peaks indicate that the unit cell is no longer monoclinic but triclinic (space group P1̄). This transition is characterized by a contraction of the monoclinic ab plane, while the c axis remains almost unchanged. There are six nonequivalent Fe sites in the triclinic cell, and the charge disproportionation magnitude is little affected.