It is well established that graphite can be transformed into superhard carbons under cold compression (Mao et al. Science 2003, 302, 425). However, structure of the superhard carbon is yet to be determined experimentally. We have performed an extensive structural search for the high-pressure crystalline phases of carbon using the evolutionary algorithm. Nine low energy polymorphic structures of sp(3)-hybridized carbon result from the unbiased search. These new polymorphic carbon structures together with previously reported low-energy sp(3)-hybridized carbon structures (e.g., M-carbon, W-carbon, and Cco-C-8 or Z-carbon) can be classified into three groups on the basis of different ways of stacking two (or more) out of five (A-E) types of buckled graphene layers. Such a classification scheme points out a simple way to construct a variety of sp(3)-hybridized carbon allotropes via stacking buckled graphene layers in different combinations of the A-E types by design. Density-functional theory calculations indicate that, among the nine low-energy crystalline structures, seven are energetically more favorable than the previously reported most stable crystalline structure (i.e., Cco-C-8 or Z-carbon) in the pressure range 0-25 GPa. Moreover, several newly predicted polymorphic sp(3)-hybridized carbon structures possess elastic moduli and hardness close to those of the cubic diamond. In particular, Z-carbon-4 possesses the highest hardness (93.4) among all the low energy sp(3)-hybridized carbon structures predicted today. The calculated electronic structures suggest that most polymorphic carbon structures are optically transparent. The simulated X-ray diffraction (XRD) spectra of a few polymorphic structures are in good agreement with the experimental spectrum, suggesting that samples from the cold compressed graphite experiments may consist of multiple polymorphic phases of sp(3)-hybridized carbon.