Minkowski decomposition conjecture for flexible polytopes

Let $P\subset\mathbb{R}^d$ be a flexible polytope, meaning that it admits a continuous deformation preserving its combinatorial type and edge lengths that is not a continuous isometry. Minkowski decomposition conjecture. There is a representation

$$P=Q_1+\cdots+Q_n$$

as a Minkowski sum of rigid polytopes $Q_i$, such that every flex of $P$ is obtained by continuously reorienting some of the $Q_i$. The source presents this as a proposed structural description of flexible polytopes; it notes that only polygons are known as elementarily flexible examples, but gives no resolution of the conjecture.