We show how to edge-unfold a new class of convex polyhedra, specifically a new class of prismatoids (the convex hull of two parallel convex polygons, called the top and base), by constructing a nonoverlapping "petal unfolding" in two new cases: (1) when the top and base are sufficiently far from each other; and (2) when the base is a rectangle and all other faces are nonobtuse triangles. The latter result extends a previous result by O'Rourke that the petal unfolding of a prismatoid avoids overlap when the base is a triangle (possibly obtuse) and all other faces are nonobtuse triangles. We also illustrate the difficulty of extending this result to a general quadrilateral base by giving a counterexample to our technique.

中文翻译：

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边缘展开棱柱体：高或矩形底座

我们展示了如何边展开一类新的凸多面体，特别是一类新的棱柱体（两个平行凸多边形的凸包，称为顶部和底部），通过在两种新情况下构造一个非重叠的“花瓣展开”： (1) 当顶部和底部相距足够远时；(2) 当底为矩形，其他面均为非钝角三角形时。后一个结果扩展了 O'Rourke 的先前结果，即当底面是三角形（可能是钝角）并且所有其他面都是非钝角三角形时，棱柱体的花瓣展开避免重叠。我们还通过对我们的技术给出一个反例来说明将这个结果扩展到一般四边形底的困难。