Let $\zeta =e^{i\pi /3}$ be a primitive sixth root of unity. Let $S$ denote all points in the complex plane of the form ${\sum }_{k=0}^5{a}_k{\zeta }^k$, where $0\le a_k\le 1$ for all $k=0,1,\dots ,5$. What is the area of $S$?