Unfoldings and Nets of Regular Polytopes

11/02/2021

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by   Satyan L. Devadoss, et al.

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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.