2 problems

Let $X\subset\mathbb R^3$ be a Delone set with mutually equivalent $2R$-clusters. For each point $x\in X$, let $S_x(2R)$ denote its local group. Weak 5-gonal symmetry conjecture. T…

Let $X\subset\mathbb R^3$ be a Delone set with parameter $R$. For each point $x\in X$, let $S_x(2R)$ be its local group, and let $Y$ be the subset of points whose local groups cont…