Ghomi proved that every convex polyhedron could be stretched via an affine transformation so that it has an edge-unfolding to a net [Gho14]. A net is a simple planar polygon; in particular, it does not self-overlap. One can view his result as establishing that every combinatorial polyhedron has a metric realization that allows unfolding to a net. Joseph Malkevitch asked if the reverse holds (in some sense of ``reverse"): Is there a combinatorial polyhedron such that, for every metric realization P in R^3, and for every spanning cut-tree T, P cut by T unfolds to a net? In this note we prove the answer is NO: every combinatorial polyhedron has a realization and a cut-tree that unfolds the polyhedron with overlap.

翻译：Ghomi证明了每个凸多面体可通过仿射变换拉伸，使得其能沿边展开为一个网格图（net）[Gho14]。网格图是一个简单平面多边形，尤其不会自重叠。可将该结果理解为：每个组合多面体都存在一个度量实现，该实现允许展开为网格图。Joseph Malkevitch 提问反向结论是否成立（在某种"反向"意义上）：是否存在一个组合多面体，使得对该多面体的每个度量实现 P ⊂ R³ 及每个生成割树（spanning cut-tree）T，经 T 切割后的 P 总能展开为网格图？本文证明答案为否：每个组合多面体均存在一个实现及一个割树，使得该多面体展开时产生重叠。