Compounds containing allenes, cumulenes and oligoynes (polyalkynes) have attracted attention for both their conformation and reactivity. Whilst the textbook molecular orbital description explains the general electronic and molecular structure of the cumulenes, there are anomalies in both the crystal structures and cycloaddition products involving oligoynes and allenes; the understanding of these molecules is incomplete. Through a computational study we elucidate that the frontier orbitals of the allene and oligoyne families are extended helices. These orbitals are the linear analogue to the Möbius aromatic systems, which also display non-linear π interactions. The axial chirality found in allenes and oligoynes is intimately related to the topology of the frontier orbitals, and has implications for predictions of cycloaddition pathways, structure stability and spectroscopy.