  We exhibit an $n$-node graph whose independent set polytope requires extended
formulations of size exponential in $\Omega(n/\log n)$. Previously, no explicit
examples of $n$-dimensional $0/1$-polytopes were known with extension
complexity larger than exponential in $\Theta(\sqrt{n})$. Our construction is
inspired by a relatively little-known connection between extended formulations
and (monotone) circuit depth.
