Centrioles make up the centrosome and basal bodies in animals and as such play important roles in cell division, signalling and motility. They possess characteristic 9-fold radial symmetry strongly influenced by the protein SAS-6. SAS-6 is essential for canonical centriole assembly as it forms the central core of the organelle, which is then surrounded by microtubules. SAS-6 self-assembles into an oligomer with elongated spokes that emanate towards the outer microtubule wall; in this manner, the symmetry of the SAS-6 oligomer influences centriole architecture and symmetry. Here, we summarise the form and symmetry of SAS-6 oligomers inferred from crystal structures and directly observed in vitro. We discuss how the strict 9-fold symmetry of centrioles may emerge, and how different forms of SAS-6 oligomers may be accommodated in the organelle architecture.