Trapezohedral Graph

The skeleton of a trapezohedron may be termed a trapezohedral graph. -trapezohedral graphs are illustrated above for  to 10 in circular embeddings with the two interior points corresponding to the trapezohedron apices. The case  corresponds to the cubical graph.

The trapezohedral graphs are bipartite, Hamiltonian, perfect, planar, polyhedral, traceable, triangle-free, and uniquely colorable.

The -trapezohedral graph has the following property counts.

property	count
cycle count
edge count
face count
Hamiltonian cycle count
Hamiltonian path count
path count
vertex count