Brandolini et al. conjectured in (Preprint, 2019) that all concrete lattice polytopes can multitile the space. We disprove this conjecture in a strong form, by constructing an infinite family of counterexamples in ℝ3 .
Garber, Alexey and Pak, Igor, "CONCRETE POLYTOPES MAY NOT TILE THE SPACE" (2020). Mathematical and Statistical Sciences Faculty Publications and Presentations. 78.