Coxeter element

Okay, so imagine you have a group of friends who all love to play a game where they move around in different patterns. Let's say they can move forward, backward, left, and right.

Now, let's say you want to figure out one special move that will make them all end up in the exact opposite spots that they started. That special move is called the Coxeter element.

It's like a secret code that you can use to make your friends do a special dance that ends up with them all swapping places with each other. Pretty cool, huh?