Some new topological properties of the triangular pyramid networks

The triangular pyramid, proposed by Razavi and Sarbazi-Azad [The triangular pyramid: Routing and topological properties, Information Sciences 180 (2010) 2328–2339], is a hierarchical structure based on triangular meshes. In this paper, we show that the triangular pyramid shares some nice symmetry properties of the pyramid. We also determine the connectivity of the triangular pyramid and prove that it is 1-fault-tolerant vertex-pancyclic.