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 semiregular polyhedron and makingsure that the corners are nicely mitered (Fig). Often the subset of edges is selected in such a way that asingle, branchless, closedloop 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. 
