Ridge-unfolding conjecture for regular convex polytopes

Let PP be a regular convex polytope, and consider a ridge unfolding obtained by cutting ridges of PP so that its facets can be unfolded into Euclidean space without overlapping. A resulting unfolding is a net if the unfolded facets form a connected, non-overlapping realization of the boundary of PP. Ridge-unfolding conjecture. Every ridge unfolding of a regular convex polytope yields a net. The paper establishes the analogous statement for cubes and notes that a similar result for simplices follows easily; the conjecture concerns the remaining regular convex polytopes and is not resolved in the supplied text.

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Primary source

Kristin DeSplinter, Satyan L. Devadoss, Jordan Readyhough and Bryce Wimberly, “Unfolding cubes: nets, packings, partitions, chords”, arXiv:2007.13266 (2020).

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