There are 88 Extended TriDrafter, which consist of three 90-60-30 triangles, which are connected at least with half an edge. TriDrafter develop a remarkable complexity by generating extremely many grid shifts. This makes them a nice target for interesting studies.
There is a similarity with the TriDom tile set, which has 88 tiles too. Moreover DiDrafter and DiDoms tile sets have the same number of 13 tiles. The similarity of the figures is funny, but has no value when looking for solutions.
The TriDrafter tile set can be divided into categories, that show the possible or forced grid shift properties of the tiles.
There are 14 simple TriDrafter, which are grid conform (type 1). Four of them are ambivalent and can be placed on a grid border or not. Grid crossing tile are called dragon tiles.
You can find pictures of all convex forms with solutions at [Vicher] TriDrafter. The results on that page could be perfectly confirmed with the Logelium solver. There are 75 solvable forms out of the 1516 possible convex forms.
Surprisingly none of 294 solutions of the convex forms comes without grid shifts. This means that there is not even one solution, where all tiles fit into a uniform triangle grid. This in turn points to the importance of grid shift handling in solution methods, when you deal with drafter tiles.
These are the nine symmetric forms and here is the complete solution set in colour version: Convex Tridrafter Forms (PDF).
Most of the extended tiles span two grids and are therefore called dragons. This main category (type 2) contains 42 tiles. They will all the time induce a grid shift when placed. The grid shifts create various dragon rings, which is the special character of the TriDrafter tiles.
There are 12 more tiles, which span two grid segments in a way that the parts are not directly connected. These tiles (type 2a) also create a grid shift when placed.
The following 20 tiles (type 3) force two grid shifts, because each of the the three drafters has a different grid orientation. These tiles are very critical for finding solutions as they are difficult to place.
Although it looks impossible at first glance, the tiles can be combined to compact forms. This picture demonstrates how the TriDrafters generate and fill a complex grid structure with a lot of dragon rings. You can see the different tile types marked with one, two or three colours. The example is using only 60 tiles of the complete set.
Without the tiles the cascaded grid structure is even more clearly visible.
It's an open question if there is a convex form solution with the complete set of all 88 Extended TriDrafter tiles. It might be possible, but looks rather difficult because of the large tile number and the many grid restrictions.