An n-sided antiprism has 2n vertices and 4n edges.
They are regular, polyhedral (and therefore by necessity also 3-vertex-connected, vertex-transitive, and planar graphs), and also Hamiltonian graphs.
Later graphs in the sequence may be named after the type of antiprism they correspond to: Although geometrically the star polygons also form the faces of a different sequence of (self-intersecting) antiprisms, the star antiprisms, they do not form a different sequence of graphs.
Other infinite sequences of polyhedral graph formed in a similar way from polyhedra with regular-polygon bases include the prism graphs (graphs of prisms) and wheel graphs (graphs of pyramids).
Other vertex-transitive polyhedral graphs include the Archimedean graphs.