In the mathematical field of graph theory, an Archimedean graph is a graph that forms the skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, and all of them are regular, polyhedral (and therefore by necessity also 3-vertex-connected planar graphs), and also Hamiltonian graphs.
Along with the 13, the set of infinite prism graphs and antiprism graphs can also be considered Archimedean graphs.
References
Archimedean graph Wikipedia(Text) CC BY-SA