  Repulsive oscillator networks can exhibit multiple cooperative rhythms,
including chimera and cluster splay states. Yet, understanding which rhythm
prevails remains challenging. Here, we address this fundamental question in the
context of Kuramoto-Sakaguchi networks of identical rotators with higher-order
coupling. Through analysis and numerics, we show that three-cluster splay
states with two distinct coherent clusters and a solitary oscillator are the
prevalent rhythms in networks with an odd number of units. We denote such
tripod patterns cyclops states with the solitary oscillator reminiscent of the
Cyclops's eye. As their mythological counterparts, the cyclops states are
giants that dominate the system's phase space in weakly repulsive networks with
first-order coupling. Astonishingly, the addition of the second or third
harmonics to the Kuramoto coupling function makes the cyclops states global
attractors practically across the full range of coupling's repulsion. At a more
general level, our results suggest clues for finding dominant rhythms in
repulsive physical and biological networks.
