  The high-density plaquette percolation model in d dimensions contains a
surface that is homeomorphic to the (d-1)-sphere and encloses the origin. This
is proved by a path-counting argument in a dual model. When d=3, this permits
an improved lower bound on the critical point p_e of entanglement percolation,
namely p_e >= \mu^-2 where \mu is the connective constant for self-avoiding
walks on Z^3. Furthermore, when the edge density p is below this bound, the
radius of the entanglement cluster containing the origin has an exponentially
decaying tail.
