Stable structures of icosahedral symmetry can serve numerous functional roles, including chemical microencapsulation and delivery of drugs and biomolecules, epitope presentation to allow for an efficient immunization process, synthesis of nanoparticles of uniform size, observation of encapsulated reactive intermediates, formation of structural elements for supramolecular constructs, and molecular computing. By examining physical models of spherical virus assembly we have arrived at a general synthetic strategy for producing chemical capsids at size scales between fullerenes and spherical viruses. Such capsids can be formed by self-assembly from a class of molecules developed from a symmetric pentagonal core. By designing chemical complementarity into the five interface edges of the molecule, we can produce self-assembling stable structures of icosahedral symmetry. We considered three different binding mechanisms: hydrogen bonding, metal binding, and formation of disulfide bonds. These structures can be designed to assemble and disassemble under controlled environmental conditions. We have conducted molecular dynamics simulation on a class of corannulene-based molecules to demonstrate the characteristics of self-assembly and to aid in the design of the molecular subunits. The edge complementarities can be of diverse structure, and they need not reflect the fivefold symmetry of the molecular core. Thus, self-assembling capsids formed from coded subunits can serve as addressable nanocontainers or custom-made structural elements.