Not all triangles are the same - Even if they look alike !

One of the old tutorials contained an unsolvabe puzzle (on purpose), to teach newbies 'how to move on'. 

It consisted only of identical triangles with (2 sides /faces), and flip - rotators.
The setup of the rotations, the triangle positions, and faces was such that the soultion pattern could never be reached, because and triangle being in the right position would always have the wrong face up.

In other words : all the triangles live in a different space than the solution demands them to be in.  

By using exactly the same triangles, but with different face & location states, if you will. we can  (and did) create puzzles where all triangles are the same, but there are two groups. Triangles from one can never be in the other. 

This is comparable to the rubiks cube, where rather obviously the edge.pieces will never become corner-pieces (doh :) )

In short : Depending on the starting position, the playground symmetries, and the rotators used it can happen that triangles cannot be in a specific location with a specific rotation (alignment)
A group of triangles consists of those triangles that are interchangeable. 
This is obvious when triangles only have a color.
When they do have faces and direction markers too, some can indeed look exactly identical, but they can NOT be exchanged !