Best Technique For 3D Cube Map

Hello,

I'm working on a top down ball rolling game. The concept is pretty simple, you have to keep the ball within a set path, without bumping into cubes.

The map you're on, is essentially a cube itself, which means that when you are approaching an edge, the ball will then start rolling on that surface (+ 90 degrees rotation).

What I want to know, is the best technique for rotating the map/player in order to achieve this?

Also, the map isn't actually a solid cube, it's more of a collection of path, in which some paths are rotated at 90 degrees, etc.

Right now, I'm using a collider trigger thats positioned at the end of the edge, so when the player enters it, the player will rotate +90 degrees.