In this work we prove that if for a pair of convex bodies $K_1, K_2 \subset \mathbb{ R}^n$, $n \geq 3$, there exists a hyperplane $H$ and two distinct points $p_1$ and $p_2$ in $\mathbb{ R}^n \setminus H$ such that for every $(n-2)$-plane $M \subset H$, there exists a reflection mapping the hypersection of $K_1$ defined by $\mathrm{ aff}\{ p_1, M\}$ onto the hypersection of $K_2$ defined by $\mathrm{ aff}\{ p_2, M\}$, then there exists a reflection which maps $K_1$ onto $K_2$.
Categories: math.MG
