A narcissist thinks people are there to admire and praise him, all their actions are directed towards this goal or with this view of people on their minds. A psychopath views others as objects that hold no value. That makes him reckless and fearless of consequences. A machiavellian does everything for the cause. If that means killing people or hurting them, it doesn’t matter to him.
Here you can see the contradiction. People can’t admire or praise you, when they mean nothing to you. Their praise would be like a constant annoying noise in the background and not something to actively seek out. People being meaningless and manipulating them for a pure goal also contradicts. The core essence of the three dark triad personality traits go against each other. Of course a person can have certain traits from these. Someone can be very manipulative and self centered. But that doesn’t make him a machiavellian or a narcissist. These terms only apply if the trait is very dominant and that doesn’t appear with more than one of these.