论文标题
急性三角，堆叠和非常不可折叠的多面体
Acutely Triangulated, Stacked, and Very Ununfoldable Polyhedra
论文作者
论文摘要
我们提出了拓扑凸的边缘 - 不合同的polyhedra的新示例，即与凸多面体相同的多面体，但不能沿着它们的边缘切割并展开成一个平面物，而没有重叠。一个例子是敏锐的三角，即，每个脸都是一个急性三角。另一个例子是堆积的，即四面体面对面粘合的结果。两个家庭都实现了另一个自然财产，我们称之为非常不可折叠：对于每个$ k $，都有一个例子，使每个非重叠的多层边缘展开至少都有$ k $零件。
We present new examples of topologically convex edge-ununfoldable polyhedra, i.e., polyhedra that are combinatorially equivalent to convex polyhedra, yet cannot be cut along their edges and unfolded into one planar piece without overlap. One family of examples is acutely triangulated, i.e., every face is an acute triangle. Another family of examples is stacked, i.e., the result of face-to-face gluings of tetrahedra. Both families achieve another natural property, which we call very ununfoldable: for every $k$, there is an example such that every nonoverlapping multipiece edge unfolding has at least $k$ pieces.
