Common net

To be a valid common net, there shouldn't exist any non-overlapping sides and the resulting polyhedra must be connected through faces.

Open problem 25.31 in Geometric Folding Algorithm by Rourke and Demaine reads:"Can any Platonic solid be cut open and unfolded to a polygon that may be refolded to a different Platonic solid?

"[2]This problem has been partially solved by Shirakawa et al. with a fractal net that is conjectured to fold to a tetrahedron and a cube.

[10] *Non-orthogonal foldings The first cases of common nets of polycubes found was the work by George Miller, with a later contribution of Donald Knuth, that culminated in the Cubigami puzzle.

All the nets follow strict orthogonal folding despite still being considered free unfoldings.