Ridge Unfolding Polytopes


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 are nets. Each ridge unfolding corresponds to a spanning tree on the dual 1-skeleton, which is the graph shown below. Source code available here.

Click on the blue nodes to draw a spanning tree to unfold the polytope.
Drag to rotate. Scroll to zoom.