2021/11/02 by Satyan L. Devadoss, Devadoss, Satyan L., Matthew Harvey +1 · 1 voice
#cs.CG #math.CO
paper · pdf · doi:10.48550/arxiv.2111.01359
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.