This review discusses from a qualitative viewpoint three-dimensional structures (hydrocarbons and carbon allotropes) that can be obtained from the 4,6,12-archimedean tiling of the Euclidean plane (graphenylene net) or that are related to subgraphs derived from the graphenylene net, insisting on helical structures called [n]heliphenes with alternating 4- and 6-membered conjugated rings. Analogies with benzenoid [n]helicenes allow proposals for non-planar heliphenerelated structures that have yet to be explored.