These two are the only completed "stars" and I actually sewed two of the blue triangles on that one. And sorry to be so dumb but do you mean to take the stars apart at the center, as in halves, or take the solid triangles off? Both Paper Princess and Madquilter seem to be saying the same thing but I'm not sure what it is, lol!
I found it interesting, by the way, that the pieced triangles are machine sewn but the two halves are sewn together by hand. Maybe whoever had these didn't fully know she she was doing either!