I've seen what I consider "kaleidoscope type blocks" with as few as three pieces and up to twenty or so. The ones with only three or four pieces have four sides, but the ones using more pieces can be made with triangles. I think the ones made with six or eight triangles are used the most often.
The units made with equilateral triangles will fit together differently than the ones made with the 67.5, 67.5, 45 degree triangles.
Interesting topic to look up: Reflection symmetry