Hybrid B3LYP and density-functional-based tight-binding (DFTB) computations on the solid-state structures and electronic properties of the C(20) fullerene monomer and oligomers are reported. C(20) cages with C(2), C(2h), C(i), D(3d), and D(2h) symmetries have similar energies and geometries. Release of the very high C(20) strain is, in theory, responsible for the ready oligomerization and the formation of different solid phases. Open [2+2] bonding is preferred both in the oligomers and in the infinite one-dimensional solids; the latter may exhibit metallic character. Two types of three-dimensional solids, the open [2+2] simple cubic and the body-centered cubic (bcc) forms, are proposed. The energy of the latter is lower due to the better oligomer bonding. The open [2+2] simple cubic solid should be a conductor, whereas the bcc solids are insulators. The most stable three-dimensional solid-state structure, an anisotropically compressed form of the bcc solid, has a HOMO-LUMO gap of approximately 2 eV and a larger binding energy than that of the proposed C(36) solid.