论文标题
每个组合多面体都可以随着重叠而展开
Every Combinatorial Polyhedron Can Unfold with Overlap
论文作者
论文摘要
Ghomi证明，每个凸多面体都可以通过仿射转化伸展，以使其对网的边缘不包裹[GHO14]。网是一个简单的平面多边形；特别是，它不会自我掩盖。人们可以将他的结果视为确定每个组合多面体都有一个指标实现，可以展开网络。 约瑟夫·马尔基维奇（Joseph Malkevitch 重叠。
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.
