  Transition-metal dichalcogenide IrTe2 has attracted attention because of
striped lattice, charge ordering and superconductivity. We have investigated
the surface structure of IrTe2, 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 5x1 and 8x1 phases appear at high
temperatures, the surface ground state has the 6x1 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.
