MS29-P02 Multidimensional crossed cube tilings Shelomo Ben-Abraham (Department of Physics, Ben-Gurion University of the Negev, Beer Sheba, Israel)email: shelomo.benabraham@gmail.comThe two-dimensional squiral (square spiral) tiling is an example of a non-pisot substitution tiling with singular continuous Fourier spectrum.   Baake and Grimm invented the crossed square lattice substitution tiling as a simple equivalent to the squiral tiling [1].  I generalize this tiling to arbitrary dimension and call it "crossed cube tiling". I explicitly show its three- and four-dimensional instances.  The method is valid in any dimension from zero to countable infinity but the size of the tiling grows exponentially and becomes quite impracticable in dimensions five and more.


[1] Baake M. & Grimm U. (2014) Ergod.Th. & Dynam. Sys. 34 (, 1077-1102.
Keywords: squiral, crossed cube tiling