Could somebody explain to me how a penrose tiling , which is not periodic, can be a cross section of a regular tiling in $5$ dimensions, which is periodic? It does not make sense to me how a periodic tiling can produce an aperiodic cross-section.
Also, are there any examples of periodic $3$-dimensional tilings that can produce an aperiodic $2$-dimensional cross section? That would greatly help to visualize the previous question. Thanks!