The bulk structure of total and partial carbo-mers of graphite, referred to as graphitynes, is investigated by first-principles calculations using the Rutgers–Chalmers nonlocal correlation functional vdW-DF2 in combination with the Cooper’s exchange functional C09. This calculation level is shown to perform well for describing graphene and graphite reference structures. The AB- and ABC-graphityne stackings are predicted to be the most stable, with interlayer distances close to the one of the graphite parent. The atomic sparsity of the 2D- and 3D-α-graphyne materials resulting from the insertion of C2 units makes them much softer than the parent graphene or graphite, respectively, but they exhibit the same large elastic anisotropy. The band structures, effective masses of charge carriers, Fermi velocities, and other electronic properties of various bulk graphyne-type carbon allotropes have been calculated and are shown to depend on the number of acetylenic-like linkages between the sp2 centers and on the stacking mode. Most of the graphitynes are predicted to be graphite-like semimetals, except the ABC-α-graphityne exhibiting a graphene-like band structure with two nonequivalent Dirac cones.