In 1525, the painter Albrecht Durer introduced the notion of a net of a polytope, and published nets for some of the Platonian and Archimedian polyhedra, along with directions about how to construct them. An unfolding of a 3-dimensional polytope P is obtained by cutting the boundary of P along a collection of edges that spans the vertex set of P and then flattening the remaining set to a polygon in the plane. An unfolding is a net if it does not overlap itself. Conversely, a simple connected plane polygon with specific folding lines is a net, if it is possible to fold it into (the boundary of) a polytope. We consider the question whether every 3-dimensional polytope has a net. Although the problem is intuitive and easy to state, and there are nets known for all regular and uniform polytopes, in general it is still unsolved. After giving an overview of related questions and conjectures about the nature or existence of nets for 3-polytopes, we present an account of our experiments wit...
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