  Kalai's $3^d$ conjecture states that every centrally-symmetric $d$-polytope
has at least $3^d$ faces. We give short proofs for two special cases: if $P$ is
unconditional (that is, invariant w.r.t. reflection in any coordinate
hyperplane), and more generally, if $P$ is locally anti-blocking. In both cases
we show that the minimum is attained exactly for the Hanner polytopes.
