  In any dimension $2n \ge 6$ we show that certain spaces of symplectic
embeddings of a polydisk into a product $B^4 \times \Bbb R^{2(n-2)}$ of a
$4$-ball and Euclidean space, are not path connected. We also show that any
pair of such nonisotopic embeddings can never be extended to the same
ellipsoid.
