SL_2-Tilings Do Not Exist in Higher Dimensions (mostly)
Laurent Demonet, Pierre‐Guy Plamondon, Dylan Rupel, Salvatore Stella, Pavel Viktorovich Tumarkin · Durham Research Online (Durham University) · 2016
We define a family of generalizations of $\operatorname{SL}_2$-tilings to higher dimensions called $\boldsymbolε$-$\operatorname{SL}_2$-tilings. We show that, in each dimension 3 or greater, $\boldsymbolε$-$\operatorname{SL}_2$-tilings exist only for certain choices of $\boldsymbolε$. In the case that they exist, we show that they are essentially unique and have a concrete description in terms of odd Fibonacci numbers.