Ridge-unfolding conjecture for regular convex polytopes

Let $P$ be a regular convex polytope, and consider a ridge unfolding obtained by cutting ridges of $P$ 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 $P$. 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.