Transition-metal dichalcogenide IrTe 2 has attracted attention because of striped lattice, charge ordering and superconductivity. We have investigated the surface structure of IrTe 2 , using low energy electron diffraction (LEED) and scanning tunneling microscopy (STM). A complex striped lattice modulations as a function of temperature is observed, which shows hysteresis between cooling and warming. While the bulk 5×1 and 8×1 phases appear at high temperatures, the surface ground state has the 6×1 phase, not seen in the bulk, and the surface transition temperatures are distinct from the bulk. The broken symmetry at the surface creates a quite different phase diagram, with the coexistence of several periodicities resembling devil's staircase behavior.