Centrioles are critical for the formation of centrosomes, cilia and flagella in eukaryotes. They are thought to assemble around a nine-fold symmetric cartwheel structure established by SAS-6 proteins. Here, we have engineered Chlamydomonas reinhardtii SAS-6-based oligomers with symmetries ranging from five- to ten-fold. Expression of a SAS-6 mutant that forms six-fold symmetric cartwheel structures in vitro resulted in cartwheels and centrioles with eight- or nine-fold symmetries in vivo. In combination with Bld10 mutants that weaken cartwheel-microtubule interactions, this SAS-6 mutant produced six- to eight-fold symmetric cartwheels. Concurrently, the microtubule wall maintained eight- and nine-fold symmetries. Expressing SAS-6 with analogous mutations in human cells resulted in nine-fold symmetric centrioles that exhibited impaired length and organization. Together, our data suggest that the self-assembly properties of SAS-6 instruct cartwheel symmetry, and lead us to propose a model in which the cartwheel and the microtubule wall assemble in an interdependent manner to establish the native architecture of centrioles.