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If you're referring to induction motor, may be it's possible if you could rearrange the stator windings, e.g. put two windings on its stator that are displaced 90° from each other. One winding is connected directly to the single-phase supply. For starting (i.e. to produce a rotating magnetic field), the other winding is connected through a capacitor to the same supply.
Instead of struggling with conversion of this motor, why not to emply a divice that changes single phase into three phase supply.
Thes devices are called VSD (variable speed drive).
They are inexpensive and commonly available in wide variety of sizes to suit 3-phase motors.
river78, do mind to share why do you wish to convert 3-phase machine to single phase? Is it because you do not have 3-phase supply? Or, is it for your own interest or assignment by your lecturer? Thanks.