Notice that those star points aren't just HALF-square triangles, but are actually (what I call) TRI-square triangles - there are 3 triangles in the one square.
These are easily made by topping an HST with a plain square, drawing your diagonal line across the already sewn diagonal, and sew on each side of the drawn line as you do the HST. When you open, press and trim, you have that tri-square triangle.
Jan in VA