Tree graph representation of Hamiltonian paths (Q1324349)

A Hamiltonian path of faces of a polyhedron consists of a sequence of adjacent faces which contains each face exactly once. This paper compares by using tree diagrams the Hamiltonian itineraries versus all possible itineraries of adjacent faces of the five regular polyhedrons. The graphs for the tetrahedron, octahedron and icosahedron are binary trees. That for the cube is a ternary tree and for the dodecahedron a quaternary tree. A visual comparison is obtained between the ``pruned'' tree, consisting only of Hamiltonian paths, and the ``bushy'' tree made up of all possible face paths.