Hamilton Path

From 'Renaissance Banff' - Bridges Conference Proceedings :

Symmetrical Hamiltonian Manifolds on Regular 3D and 4D Polytopes

Carlo H. Séquin
Path-based sculptures by K. Verhoeff and R. Roelofs
The edges of the regular polytopes in three and higher dimensional spaces form highly symmetrical graphs. The edge graphs of the 3D Platonic and Archimedean solids have stimulated some artists, such as K. Verhoeff and R. Roelofs, to build impressive constructivist sculptures by sweeping a regular polygonalcross section along some or all of the edges (or cords) of a regular or semi-regular polyhedron and makingsure that the corners are nicely mitered (Fig). Often the subset of edges is selected in such a way that asingle, branchless, closed-loop path results. A sequence of edges that visits all the vertices of a graphexactly once is called a Hamiltonian path, or a Hamiltonian cycle if the path closes into a loop.