Regime, a noun, refers to a government, usually an authoritarian one.
- The country underwent regime change on its own terms.
Regimen, a noun, refers to a therapeutic treatment, usually including diet and exercise.
- The benefits of a daily fitness regimen are endless.
Regiment, as a noun, refers to a military unit or large group of people; as a verb, it means to direct or command.
- The people’s good wishes went to the soldiers of our regiment.
- They sought to regiment the people and their property.