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Let M be a d × d real contracting matrix. 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 $\left|detM\right|\ge 2^{-1/d}$, then the attractor $A_M$ has non-empty interior. We also consider the set ${}_M$ 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 ${}_M$ is positive. For this special class the full description of ${}_M$ is given as well. This paper continues our work begun...

Given a monic degree $N$ polynomial $f\left(x\right)\in \mathbb{Z}\left[x\right]$ and a non-negative integer $\ell$, we may form a new monic degree $N$ polynomial $f_{\ell }\left(x\right)\in \mathbb{Z}\left[x\right]$ by raising each root of $f$ to the $\ell$th power. We generalize a lemma of Dobrowolski to show that if $m\<n$ and $p$ is prime then $p^{N(m+1)}$ divides the resultant of $f_{p^m}$ and $f_{p^n}$. We then consider the function $(j,k)\mapsto Res(f_j,f_k)mod{p}^m$. We show that for fixed $p$ and $m$ that this function is periodic in both $j$ and $k$, and exhibits high levels of symmetry. Some discussion of its structure as a union of lattices is also given.