In 1525, Albrecht Dürer represented polytopes by cutting them open along edges and then flattening the surface onto the plane, without overlaps and without distorting the individual faces. Self-intersections are allowed during the unfolding process, but the final flattened surface must be free of overlaps. Whether a non-overlapping edge unfolding, as defined above, is possible for any complex polytopes was formulated by Shephard as a conjecture in 1975.
[D] A. Dürer, Unterweysung der Messung mit dem Zyrkel und Rychtscheyd. Nürnberg (1525). English translation with commentary by Walter L. Strauss The Painter's Manual, New York (1977).
[O] J. O'Rourke, How to fold it, Cambridge University Press, 2011, Book website
[P] K. Polthier Imagining maths- unfolding polyhedra
*[S] G.C. Shephard, Convex Polytopes with Convex Nets. Math. Proc. Camb. Phil. Soc., 78:389-403 (1975).
* indicates original appearance(s) of problem.