Let $\omega=-\frac{1}{2}+\frac{1}{2}i\sqrt{3}$. Let $S$ denote all points in the complex plane of the form $a+b\omega+c\omega^2$, where $0\le a\le 1$, $0\le b\le1$, and $0\le c\le 1$. What is the area of $S$?