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We report the appearance of a scroll ring and scroll toroid chimera statesfrom the proposed initial conditions for the Kuramoto model of coupled phaseoscillators in the 3D grid topology with inertia. The proposed initialconditions provide an opportunity to obtain as single as well as multiplescroll ring and toroid chimeras with different major and minor diameters. Weanalyze their properties and demonstrate, in particular, the patterns ofcoherent, partially coherent, and incoherent scroll ring chimera states withdifferent structures of filaments and chaotic oscillators. Those patterns cancoexist with solitary states and solitary patterns in the oscillatory networks.

Scroll ring chimera states in oscillatory networks