The tubulin-containing cytoskeleton of the human parasite Toxoplasma gondii includes several distinct structures: the conoid, formed of 14 ribbon-like tubulin polymers, and the array of 22 cortical microtubules (MTs) rooted in the apical polar ring. Here we analyze the structure of developing daughter parasites using both 3D-SIM and expansion microscopy. Cortical MTs and the conoid start to develop almost simultaneously, but from distinct precursors near the centrioles. Cortical MTs are initiated in a fixed sequence, starting around the periphery of a short arc that extends to become a complete circle. The conoid also develops from an open arc into a full circle, with a fixed spatial relationship to the centrioles. The patterning of the MT array starts from a "blueprint" with ∼five-fold symmetry, switching to 22-fold rotational symmetry in the final product, revealing a major structural rearrangement during daughter growth. The number of MT is essentially invariant in the wild-type array, but is perturbed by the loss of some structural components of the apical polar ring. This study provides insights into the development of tubulin-containing structures that diverge from conventional models, insights that are critical for understanding the evolutionary paths leading to construction and divergence of cytoskeletal frameworks.