Recent experiments reported a substantial toughening of nanotwinned diamond (nt-diamond) composite with coherently interfaced diamond polytypes (different stacking sequences). This discovery emphasizes the diversity of graphite-like structures in carbon onion precursors for synthesizing nt-diamond composite. We designed five new graphitic polytypes to investigate structural diversity in graphitic systems. Under ambient pressure, the energies of all the proposed polytypes are between those of graphite (AB structure) and a previously predicted AA structure. Dynamic and elastic stability results showed that four structures (AB'C', AB'D', AAB and ABCB) can be stable under ambient pressure. These four structures all have a large interlayer distance comparable to those in carbon onion and turbostratic graphite. Chiral graphitic structures (AB'D' and AB'C') with reversible electrical properties under slight stress might be responsible for the controversy about the bandgap of graphitic samples. Therefore, these four structures are most likely to be a part of the structures existing in carbon onion and turbostratic graphite or are structural defects in graphitic samples.