I first recognized the character trinity and its power in the original STAR TREK.
Kirk, Spock, and McCoy were an ideal heart, mind, and action trinity. When a problem needed to be solved, Spock was the logical mind, McCoy the emotional heart, and Kirk took both and created the ideal action.
These characters can also be considered a thesis, antithesis, and synthesis. Two opposite sides of a problem from Spock and McCoy, and Kirk pulling both together to find the solution.
Harry Potter, Hermione, and Ron are also a character trinity.
Three major characters like this can be a very powerful means of telling a story because they are not only working together but also working against each other. They can even reflect the complex nature of the book’s world or the moral dilemma of the story.
A love triangle in a romance is almost never a character trinity because the conflict is about the relationships, not the way these characters react together in the real world.
Instead, use the character trinity in more world-based stories like fantasy, science fiction, or adventure novels.
If you decide to use a character trinity, your main character must always be the action taker or the synthesis. The other two tend to be either passive or reactive which makes a very poor hero.