We report recent progress in the problem of distinguishing convex subsets of
cyclotomic model sets Λ by (discrete parallel) X-rays in prescribed
Λ-directions. It turns out that for any of these model sets
Λ there exists a `magic number' mΛ​ such that any two
convex subsets of Λ can be distinguished by their X-rays in any set
of mΛ​ prescribed Λ-directions. In particular, for
pentagonal, octagonal, decagonal and dodecagonal model sets, the least possible
numbers are in that very order 11, 9, 11 and 13.Comment: 6 pages, 1 figure; based on the results of arXiv:1101.4149 [math.MG];
presented at Aperiodic 2012 (Cairns, Australia