  For a virtual $n$-link $K$, we define a new virtual link $VD(K)$, which is
invariant under virtual equivalence of $K$. The Dehn space of $VD(K)$, which we
denote $DD(K)$, therefore has a homotopy type which is an invariant of $K$. We
show that the quandle and even the fundamental group of this space are able to
detect the virtual trefoil. We also consider applications to higher-dimensional
virtual links.
