  In this paper we give a simple, explicit construction of polytopal bounded
remainder sets of all possible volumes, for any irrational rotation on the $d$
dimensional adelic torus $\mathbb{A}^d/\mathbb{Q}^d$. Our construction involves
ideas from dynamical systems and harmonic analysis on the adeles, as well as a
geometric argument that reduces the existence argument to the case of an
irrational rotation on the torus $\mathbb{R}^d/\mathbb{Q}^d$.
