Discrete Tomography: Magic Numbers for N-Fold Symmetry

We consider the problem of distinguishing convex subsets of n-cyclotomic model sets Λ by (discrete parallel) X-rays in prescribed Λ-directions. In this context, a 'magic number' $m_{Λ}$ has the property that any two convex subsets of Λ can be distinguished by their X-rays in any set of $m_{Λ}$ prescribed Λ-directions. Recent calculations suggest that (with one exception in the case n=4) the least possible magic number for n-cyclotomic model sets might just be N+1, where N=lcm(n,2).