In the present study, isolated mixing regions (IMRs) in an agitated vessel using a paddle or disk-turbine impeller have been visualized experimentally, and their structural properties and formation mechanism are investigated in detail. A set of thin filaments spirally wrapping around the core of a toroidal isolated mixing region is observed under laminar-flow conditions, where the Reynolds number is smaller than 60. This filament rotates in both directions of horizontal and vertical circulating flows. The three-dimensional geometrical structure of a filament in an IMR depends on the periodical perturbations caused by the rotating impeller. We have succeeded in the determination of the three-dimensional geometrical structure of a filament in an IMR based on the relationship between the movement of a fluid particle and filament numbers and/or wire turns. Interestingly, the wire turns of filaments are opposite to movement of fluid particles.