Hamiltonian cycles on an icosidodecahedron, using the same Bézier curve rounding approach as before. I'd thought about the Hamiltonian ones at some point earlier, but I couldn't find a fast algorithm for generating them. Then Anton Bakker (@antonbakkersculptor) mentioned them after seeing my last post's Eulerian ones. Well, I looked at the algorithms again, and I realized that a basic backtracking recursion could work with a lot of common polyhedra. For the icosidodecahedron with 30 vertices and

Cycloid-Evolute