AMC 12 2016b Problem 23

What is the volume of the region in three-dimensional space defined by the inequalities $|x|+|y|+|z|\le1$ and $|x|+|y|+|z-1|\le1$?

\textbf{(A)}\ \frac{1}{6} \textbf{(B)}\ \frac{1}{4} \textbf{(C)}\ \frac{1}{3} \textbf{(D)}\ \frac{1}{2} \textbf{(E)}\ 1