  We use low-energy electron microscopy (LEEM), low-energy electron diffraction
(LEED) and scanning tunneling microscopy (STM) to study different orientations
of single-layer graphene sheets on Ir(111). The most-abundant orientation has
previously been characterized in the literature. Using selective-area LEED we
find three other variants, which are rotated 14, 18.5 and 30 degrees with
respect to the most common variant. The about 30-degree-rotated structure is
also studied by STM. We propose that all 4 variants are moire structures that
can be classified using simple geometric rules involving periodic and
quasi-periodic structural motifs. In addition, LEEM reveals that linear defects
form in the graphene sheets during cooling from the synthesis temperature. STM
shows that these defects are ridges, suggesting that the graphene sheets
delaminate locally as the Ir substrate contracts.
