April 26th 2018 - The different faces of chimera states Oscillatory networks play a crucial role in the understanding of complex systems such as the brain or electric power grids. Such networks may exhibit a vast variety of different dynamical phenomena, the underlying mechanisms of which still raise many questions. These phenomena include so-called chimera states, extraordinary chaotic states in which some of the oscillators show synchronized motion, whereas some others behave incoherently. Even these states might occur in different variations on which we shed some light in this letter. Starting from very small networks of just four oscillators, we show that one can distinguish such chimera states using symmetry arguments: Some chimeras behave in a way which leaves the dynamical structure unchanged when some of the oscillators are interchanged, whereas other chimera states do not have that particular invariance. This difference in the symmetry properties may also be used to distinguish between states in larger ensembles of coupled oscillators. Our results might help elucidating dynamics of partial synchrony occurring in nature, for example during unihemispheric sleep in certain animals. For the full article preprint, see here.