Trinagon puzzles are built from symmetry. The key is to understand which symmetry is actually at work.

Take the TStar. Remove the spike rotators. The remaining rotators are hexagonal.
Eg. 6 triangles around each rotator & a 2-fold overlaps between each rotator. Exactly like a hexagon playground.

So it's reasonable to assume we deal with a hexagonal puzzle.

Locally around each rotator this is correct. As long as you only use two rotators it  still is.
Globally it is not : The spikes fold the hexagon in half.  

A triangle has to move around a spike twice to come to the same state (face & direction), as moving once around the hex-rotators.
This holds true regardless of which rotators are in play.

It's one of those things that are (maybe only) obvious once they are known.

And this opens the door for some very tricky puzzles.