Many stars can look the same (or just very similar) but are different depending on how they are constructed. It happens that I'm working on a Lemoyne star block now in the Virtual Quilting Weekend thread.
Virtual quilting weekend—April 10-12, 2020
It has diamond shapes for the star blades but you can achieve the same look with more seams and HST (half square triangles). I will also be setting in the corner square as a square, the current trend is to divide that into two triangles and sew down the diagonals. A purist would say that isn't a Lemoyne Star, I think the whirling star blades are the important part more than the background. I'm also planning on piecing the triangles as a single unit and not the simpler triangles down the seam line.
Only six blocks, a good chance for me to work on my precision sewing and probably enough to say "next time I use the triangles!"