The formation mechanism of polycyclic aromatic hydrocarbons (PAR) with three fused aromatic rings starting from naphthalene has been studied using accurate ab initio G3(MP2,CC)//B3LYP/6-311G** calculations followed by the kinetic analysis of various reaction pathways and computations of relative product yields. The results reveal new insights into the classical hydrogen abstraction-C2H2 addition (HACA) scheme of PAH growth. The HACA mechanism has been shown to produce mostly cyclopentafused PAHs instead of PAHs with six-member rings only, in contrast to the generally accepted view on this mechanism. Considering naphthalene as the initial reactant, the HACA-type synthesis of higher PAHs with all six-member rings, anthracene and phenanthrene, accounts only for 3-6% of the total product yield at temperatures relevant to combustion (1000-2000 K), whereas cyclopentafused PAHs, including acenaphthalene (41-48%), 4-ethynylacenaphthalene (similar to 14%), 3-ethynylacenaphthalene 1-methylene-1H-cyclopenta[b]naphthalene (similar to 6%), and 3-methylene-3H-cyclopenta[a] naphthalene (similar to 5%), account for another similar to 75%. It has been shown that acetylene addition to the radical site adjacent to the bay region in naphthalene (as in 1-naphthyl radical) or other similar PAH with a bay region is highly unlikely to be followed by the addition of a second acetylene molecule; alternatively, the bay region closure with a buildup of a new five-member ring occurs. Acetylene addition to a nonbay carbon atom (as in 2-naphthyl radical) can be followed by the second acetylene addition only at T < 1000 K, producing anthracene and phenanthrene. However, at temperatures relevant to combustion, such pathways give negligible contributions to the total product yield, whereas the dominant reaction product, 2-ethynylnaphthalene, is formed by simple hydrogen atom elimination from the attached ethenyl group. An additional six-member ring buildup may occur only after intermolecular hydrogen abstraction from ethynyl-substituted PAR (2-ethynylnaphthalene), in particular, from the carbon atoms adjacent to the existing ethynyl (C2H) fragment, followed by C2H2 addition producing adducts with two ethynyl C2H and ethenyl C2H2 groups next to each other, which then undergo a fast six-member ring closure. Nevertheless, this process has been shown to be relatively minor (similar to 25%), whereas the major process is a five-member ring closure involving the same C2H and C2H2 groups and leading to a cyclopentafused PAH molecule. Although the computed product yields show a good agreement with experimentally observed concentrations of acenaphthalene and anthracene in various aliphatic and aromatic flames, the yield of phenanthrene, which exhibits an order of magnitude higher concentration than anthracene both in combustion flames and environmental mixtures, via the considered pathways is significantly underpredicted. This result points at the possible existence of another mechanism responsible for the formation of phenanthrene and other all-six-member-ring PAHs. The overall kinetic scheme for the HACA buildup process leading to various three-ring PAHs (both with six-member rings only and cyclopentafused) from naphthalene, which can be included in flame kinetic models, has been constructed, with rate constants for all individual reaction steps provided.