The defects of a system where hexagons and rolls are both stable solutions are considered. On the basis of topological arguments we show that the unstable phase is present in the core of the defects. This means that a roll is present in the penta-hepta defect of hexagons and that a hexagon is found in the core of a grain boundary connecting rolls with different orientations. These results are verified in an experiment of thermal convection under non-Boussinesq conditions. PACS numbers: 47.20. Bp, 47.25.Qv Defects play an important role in the dynamics of pattern-forming systems. Specifically, dislocations and grain boundaries in convective patterns of rolls, and spirals and centered defects in chemical reactions, have been the object of several studies. ! However, the structure of defects has not been carefully analyzed in systems where two different symmetries coexist. This is a very important case that appears very often in nature, a typical example being the transition between hexagons and rolls in thermal convection. The competition between patterns associated with different symmetries has recently been discussed on the basis of general arguments. 2 The purpose of this Letter is to study defect properties when hexagons and rolls are stable solutions in a nonequilibrium pattern-forming system.The competition between hexagons and rolls can be described by means of three coupled Ginzburg-Landau equations (GLH), which determine the behavior of the three complex amplitudes A t of the sets of rolls describing the hexagonal structure. Each of them makes an angle of 2;r/3 with each of the others. A qualitative description of the nature of the cores of the various defects which may be observed in this problem can be deduced 3 from an elementary study of the following sixdimensional dynamical system, obtained from GLH, in the limit of homogeneous patterns: 4 d

The selection and competition of Turing patterns in the Brusselator model are reviewed. The stability of stripes and hexagons towards spatial perturbations is studied using the amplitude equation formalism. For hexagonal patterns these equations include both linear and nonpotential spatial terms enabling distorted solutions. The latter modify substantially the stability diagrams and select patterns with wave numbers quite different from the critical value. The analytical results from the amplitude formalism agree with direct simulations of the model. Moreover, we show that slightly squeezed hexagons are locally stable in a full range of distortion angles. The stability regions resulting from the phase equation are similar to those obtained numerically by other authors and to those observed in experiments.