On self-affine tiles whose boundary is a sphere

Jörg Thuswaldner, Shu-qin Zhang

Let $M$ be a $3\times 3$ integer matrix each of whose eigenvalues is greater than $1$ in modulus and let $\mathcal{D}\subset {\mathbb{Z}}^3$ be a set with $|\mathcal{D}|=|\det M|$, ca…