Over a decade ago, it was shown that every edge unfolding of the Platonic solids was without self-overlap, yielding a valid net. We consider this property for regular polytopes in arbitrary dimensions, notably the simplex, cube, and orthoplex. It was recently proven that all unfoldings of the $n$-cube yield nets. We show this is also true for the $n$-simplex and the $4$-orthoplex but demonstrate its surprising failure for any orthoplex of higher dimension.

翻译：10多年前,人们发现,等离子体固体的每一个边缘都没有自我重叠,产生一个有效的网。我们认为,这种特性对于任意性的常规多面形,特别是简单化、立方体和正方形。 最近,人们证明,美元立方体产量网的所有亮点都是以美元为单位的。 美元简单化和4美元双倍化也是这样,但是,我们却显示了它对于任何更高尺寸的圆形的出人意料的失败。