We can unfold a 3D polyhedron by cutting along its edges and laying its connected faces on the 2D plane. When faces do not overlap, the result is called a net
Similarly, a 4D polytope can be unfolded into 3D space by cutting along its ridges. Beautifully, all unfoldings of the 4-cube
, 4-simplex, and 4-orthoplex
Each ridge unfolding corresponds to a spanning tree
on the dual 1-skeleton
, which is the graph shown below.
Source code available here