Is there a name for a polygon in which you could place a light bulb that would light up all of its area? (for which there exists a point so that for all points inside it the line connecting those two points does not cross one of its edges)
Examples of “lightable” polygons:
Examples of “unlightable” polygons:
Yes, those are called star-shaped polygons. They have numerous applications in mathematics, for example in complex analysis.