可逆多面体网
Reversible Nets of Polyhedra
摘要：
一个可逆（或铰链由内而外可变形）图形的例子是杜德尼的哈伯达舍之谜，其中一个等边三角形被分成四块，然后像链条一样铰接，然后通过旋转铰接的块转化为正方形。此外，每个图形的整个边界进入另一个图形的内部，并成为另一个图形的解剖线。在以往的研究中，人们已经发现了许多有趣的图形还原结果，但大多数都是多边形上的结果。本文将这些结果推广到更广泛的一般连通图。证明了任意凸多面体的曲面沿不相交的剖分树剖分得到的两个网是可逆的。此外，还给出了一个等四面体的两个网同时是可逆的和镶嵌的条件。
英文摘要：
An example of reversible (or hinge inside-out transformable) figures is the Dudeney's Haberdasher's puzzle in which an equilateral triangle is dissected into four pieces, then hinged like a chain, and then is transformed into a square by rotating the hinged pieces. Furthermore, the entire boundary of each figure goes into the inside of the other figure and becomes the dissection lines of the other figure. Many intriguing results on reversibilities of figures have been found in prior research, but most of them are results on polygons. This paper generalizes those results to a wider range of general connected figures. It is shown that two nets obtained by cutting the surface of an arbitrary convex polyhedron along non-intersecting dissection trees are reversible. Moreover, a condition for two nets of an isotetrahedron to be both reversible and tessellative is given.
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