Something I’ve noticed when tessellating with circular rosette parts:

The smallest two units (or just one, when N is even) are a bit tricky — they increase the net length of convex arcs along the boundary (i.e., the total convex arc length minus the concave arc length). To include them in a uniformly dense way, the net length of convex arcs seems to grow as Ω(R²), while the boundary itself grows only as O(R), given a radius R. I suspect that makes it infeasible.

Note that in this periodic example, the smallest two units appear only along the central line.