The three phase auto transformer is a combination of three single phase autotransformers. It has three windings, one per phase.
Using a rotary contact which moves over each winding, we can change the 3-phase output voltage. Thus it is possible to vary the three phase output with a single rotary knob. (See Fig. 1(a)). Fig. 1(b) shows the electrical connections of the three windings. One end of all the windings is connected together. The other ends are connected to the 3 phase ac supply (R, Y, B). The variable point of each winding is brought out as output (r, y, b points in Fig. 1(b)). The dotted line in Fig. 1(b) shows that all the rotary (sliding) contacts are mechanically coupled to each other so that only one controlling knob can control the output voltage. As we move the sliding contact on each winding, the voltage XV will change.