A strongly nonperiodic tiling is defined as a tiling that does not admit infinite cyclic symmetry. The purpose of this article is to construct, up to isomorphism, uncountably many strongly nonperiodic hyperbolic tilings with a single vertex configuration by a hyperbolic rhombus tile. We use a tile found by Margulis and Mozes , which admits tilings, but no tiling with a compact fundamental domain.
"Strongly nonperiodic hyperbolic tilings using single vertex configuration." Hiroshima Math. J. 48 (2) 133 - 140, July 2018. https://doi.org/10.32917/hmj/1533088825