The seven-direction conjecture for convex subsets of three-dimensional Delone sets

Let $\varLambda\subset\mathbb R^3$ be a Delone set. A set of $\varLambda$-directions is in general position when any three directions from it span the whole $3$-space. Seven-direction conjecture. The convex subsets of $\varLambda$ can be distinguished by the X-rays in any set of seven $\varLambda$-directions in general position. This conjecture is motivated by a continuous version formulated by Gardner in 1995; the three-dimensional discrete-tomography problem remains open in the stated generality.