Nanometre-sized objects with highly symmetrical, cage-like polyhedral shapes, often with icosahedral symmetry, have recently been assembled from DNA1–3, RNA4 or proteins5,6 for applications in biology and medicine. These achievements relied on advances in the development of programmable self-assembling biological materials7–10, and on rapidly developing techniques for generating three-dimensional (3D) reconstructions from cryo-electron microscopy images of single particles, which provide high-resolution structural characterization of biological complexes11–13. Such single-particle 3D reconstruction approaches have not yet been successfully applied to the identification of synthetic inorganic nanomaterials with highly symmetrical cage-like shapes. Here, however, using a combination of cryo-electron microscopy and single-particle 3D reconstruction, we suggest the existence of isolated ultrasmall (less than 10 nm) silica cages (‘silicages’) with dodecahedral structure. We propose that such highly symmetrical, self-assembled cages form through the arrangement of primary silica clusters in aqueous solutions on the surface of oppositely charged surfactant micelles. This discovery paves the way for nanoscale cages made from silica and other inorganic materials to be used as building blocks for a wide range of advanced functional-materials applications. Machine-learning algorithms are used to generate single-particle three-dimensional reconstructions, revealing that highly symmetrical dodecahedral silica cages, around 10 nm in size, self-assemble in the presence of surfactant micelles.