Cypoviruses and baculoviruses are notoriously difficult to eradicate because the virus particles are embedded in micrometre-sized protein crystals called polyhedra. The remarkable stability of polyhedra means that, like bacterial spores, these insect viruses remain infectious for years in soil. The environmental persistence of polyhedra is the cause of significant losses in silkworm cocoon harvests but has also been exploited against pests in biological alternatives to chemical insecticides. Although polyhedra have been extensively characterized since the early 1900s, their atomic organization remains elusive. Here we describe the 2 A crystal structure of both recombinant and infectious silkworm cypovirus polyhedra determined using crystals 5-12 micrometres in diameter purified from insect cells. These are the smallest crystals yet used for de novo X-ray protein structure determination. We found that polyhedra are made of trimers of the viral polyhedrin protein and contain nucleotides. Although the shape of these building blocks is reminiscent of some capsid trimers, polyhedrin has a new fold and has evolved to assemble in vivo into three-dimensional cubic crystals rather than icosahedral shells. The polyhedrin trimers are extensively cross-linked in polyhedra by non-covalent interactions and pack with an exquisite molecular complementarity similar to that of antigen-antibody complexes. The resulting ultrastable and sealed crystals shield the virus particles from environmental damage. The structure suggests that polyhedra can serve as the basis for the development of robust and versatile nanoparticles for biotechnological applications such as microarrays and biopesticides.