Spent far too long today trying to fill an 11-sided hole using only corner-to-corner quadrilaterals (id Tech 4 patch geometry, don't ask) and got that familiar uneasy feeling of "there is a mathematical proof somewhere out there that could've told you this was futile".
The problem with making shapes all day is that you start to pride yourself on your ability to make any shape, forgetting that there are in fact Forbidden Shapes that cannot be.
for a moment i also thought this might be possible, but then i woke up slightly and i'm pretty sure it's not. 11-sided polygons have a total interior angle sum of (11-2)*180=1620 degrees, and quadrilaterals have an interior angle sum on 360 degrees, so there's no way to divide the interior angles evenly. both those numbers can be derived in a variety of ways but i like that they're a consequence of ear cutting: https://en.wikipedia.org/wiki/Two_ears_theorem