  Let $M$ be a $d\times d$ contracting matrix. In this paper we consider the
self-affine iterated function system $\{Mv-u, Mv+u\}$, where $u$ is a cyclic
vector. Our main result is as follows: if $|\det M|\ge 2^{-1/d}$, then the
attractor $A_M$ has non-empty interior.
  We also consider the set $\mathcal U_M$ of points in $A_M$ which have a
unique address. We show that unless $M$ belongs to a very special (non-generic)
class, the Hausdorff dimension of $\mathcal U_M$ is positive. For this special
class the full description of $\mathcal U_M$ is given as well.
  This paper continues our work begun in two previous papers.
