Can I use three-phase stepper motors with pololu style stepper drivers? If not, what kind of drivers support three-phase motors?
Three phase stepper motors are superior in several ways: see this advertising literature. Unfortunately for using this with simple stepper drivers, they have an extra coil of wire that simple drivers have no way to control. Two phase motors have two isolated coils, while three phase motors have three coils connected in a star configuration.
Texas Instruments offers this design suggestion for using three-phase motors: TI White Paper. Ultimately, it is driven by three synchronized PWM signals connected to three H-bridges, each driving one of the three motor wires. One could build a board with a micro-controller that accepted step and direction pulses and output the three-phase drive. At that level, you could substitute the micro-control-plus-H-bridge board for the Pololu-style driver in an existing 3D printer framework. You would need to configure the steps-per-mm correctly for the new drive system.
If you did this, and the sales literature is correct, you should get quieter operation with higher torque. How that would affect operation would depend on the torque of the motor, the rotating mass of the motor, and the gearing or belt drive you use.
Like two-phase motors, high torque at high speed requires driving the motor with a voltage much higher than the "specified" steady-state motor voltage.
You can use 3 phase stepper motors for 3D printers but I have not seen a Pololu-style driver. You can use an external driver like the 3DM580S. Many 3D printer control boards offer external connections to send steps(or pulses)/direction/enable/ground connection to an external driver. The 3-phase motors that I have seen tend to be bigger, which means that you'll need bigger belts. Also, they move 1.2 degrees per whole step, as opposed to the typical 1.8 degrees per step with bipolar stepper motors (0.9 degrees/step bi-polar motors are common as well). This means you'll need to make some slight adjustments to the steps/mm on your firmware but that's not too difficult.
3D printers typically use bipolar two-phase stepper motors, and it is possible that Pololu-style carriers for stepper-motor drivers only support such motors.
Certainly, drivers for three-phase stepper motors exist, for example, the Trinamic TMC5062, but I cannot find any Pololu-style carriers for this chip. Even if a Pololu-style carrier can be sourced, it is not certain that existing 3D-printer firmware can be configured to control it.
If you are thinking about re-purposing some three-phase motors, I would advise that you purchase standard bipolar motors, instead. Bipolar two-phase motors suitable for 3D printing are not that expensive.