Yeah, I mean 12! is ~479 million, and there are 20 vertices, so that is very much within brute-force-on-a-laptop range. For some net, I think given a vertex + l

Yeah, I mean 12! is ~479 million, and there are 20 vertices, so that is very much within brute-force-on-a-laptop range. For some net, I think given a vertex + list of faces, there is a simple-to-get yes/no answer on whether a ray passing through the faces and returning to the vertex exists. I wonder if you can just write a Python script to do it... Edit: Even simpler - there are 43,380 nets of a dodecahedron, and each has 20 vertices. So if you just draw ~8 million straight lines and see if any are both on the net and do not intersect another vertex, you'll find (at least) one that works!