Caveolae are invaginated plasma membrane domains involved in mechanosensing, signaling, endocytosis, and membrane homeostasis. Oligomers of membrane-embedded caveolins and peripherally attached cavins form the caveolar coat whose structure has remained elusive. Here, purified Cavin1 60S complexes were analyzed structurally in solution and after liposome reconstitution by electron cryotomography. Cavin1 adopted a flexible, net-like protein mesh able to form polyhedral lattices on phosphatidylserine-containing vesicles. Mutating the two coiled-coil domains in Cavin1 revealed that they mediate distinct assembly steps during 60S complex formation. The organization of the cavin coat corresponded to a polyhedral nano-net held together by coiled-coil segments. Positive residues around the C-terminal coiled-coil domain were required for membrane binding. Purified caveolin 8S oligomers assumed disc-shaped arrangements of sizes that are consistent with the discs occupying the faces in the caveolar polyhedra. Polygonal caveolar membrane profiles were revealed in tomograms of native caveolae inside cells. We propose a model with a regular dodecahedron as structural basis for the caveolae architecture.