We achieve a systematic modeling of all rovibrational levels in the (C2H2)-C-12 ((X) over tilde (1) Sigma(g)(+)) molecule, which is tested up to the near infrared range. It is based on the cluster picture, which was demonstrated to block diagonalize the full vibrational energy matrix, and to allow unraveling the vibrational energy pattern in (C2H2)-C-12, up to 12 000 cm(-1) [see M. Abbouti Temsamani and M. Herman, J. Chem. Phys. 102, 6371 (1995)]. Each of those clusters, which are called here V-clusters, is made of pure vibrational type diagonal and off-diagonal matrix elements. That model is extended to take care of the rotational structure, defining the V/l/C-cluster model. In a first step J-dependent terms are included in the diagonal elements of the V-clusters, and rotational l resonance off-diagonal matrix elements are included, leading to couple specific V-cluster matrices, resulting into so-called V/l-clusters. This extension is quantitatively demonstrated to reproduce the reported effective principal rotational constant and effective higher order distortion constants, for four selected clusters of levels : those containing V-1 + V-3, V-1 + V-2 + V-3. 3V(3) and V-2 + 3V(3). In the case of the 3v(3) range, new FTIR spectra recorded around 9700 cm(-1) are used. The related experimental conditions and new observed spectral features are briefly presented. A further extension of the model is then accomplished to include Coriolis-type interaction, by coupling V/l-clusters using a systematic mechanism. That step, defining the model of V/l/C-clusters, allows to suggest assignment for extra rovibrational lines observed around 3v(3) Those various steps are supported by a consistent picture involving constants of the motion, starting with three pseudoquantum numbers in the case of V-cluster, {n(s),n(r),k}, from which two, {n(s),n(r)} and then one {n(r)} remain when defining respectively the V/l-cluster and V/l/C-cluster matrices.