If i take a lens, like a vesica piscis (or a skinnier version) and copy it, and rotate the copy 90 degrees, i get a 4 pointed object, but the lines are all curved.
This shape is identical to what i might get if i drew a regular straight lined 4 point star on a balloon and inflated the balloon, but I don't know what this star shape is called, or how to find more information on it. It reminds me of the arcs in Cathedrals but i wasn't able to find it in a cathedral iconography list.