A family of crystal structures of carbon composed of alternating sp2 and sp3 bonds is investigated. Graphitic strips are connected by sp3 bonds to form an array of hexagonal pillars exhibiting a honeycomb lattice in the perpendicular plane. The electronic structure and elastic properties of this family of structures are calculated using an ab initio pseudopotential as well as the environment-dependent tight-binding method. Their electronic structure has a similar size dependence to zigzag nanotubes; they are metallic if twice the strip width is a multiple of three hexagonal units, and otherwise semiconducting with a wider range of the band gap than for carbon nanotubes. The structural stability is studied and compared with other carbon structures.