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

Discrete tomography: Magic numbers for $N$-fold symmetry