Traversals of polyhedra

Traversals of polyhedra involve finding paths or cycles along the edges, vertices, or faces of a polyhedron, such as Eulerian paths (using each edge once) or Hamiltonian cycles (visiting each vertex once).

Important properties

• An Eulerian path is a path that uses every edge of the polyhedron exactly once.

• A Hamiltonian cycle is a cycle that visits every vertex exactly once and returns to the starting point.

• Not all polyhedra have Eulerian paths or Hamiltonian cycles.

• The structure of the polyhedron (like the number of edges at each vertex) affects what traversals are possible.