Under consideration is a polycrystal model made of similar space-filling grains, which have a realistic polyhedral shape. Active slip systems in each constitutive crystal are selected one by one to ensure the least strain rate misfit on interfaces between immediate neighbors, keeping a prescribed strain rate for the whole aggregate. Residual strain rate variation among disoriented crystals depends on their shape (mutual coordination) and on how many slip systems are considered active in each of them. Each grain spin in interaction with differently deformed neighbors is derived by means of compatibility equation, involving both the strain and rotation. Thereby predicted rolling texture of fcc polycrystal, as compared with that by the Taylor model, proved to be closer to experimental data. Another advantage of the proposed model is no ambiguity in selecting slip pattern of constitutive crystals. The approach, explicitly taking into account the shape and coordination of interacting grains, is aimed to partly substitute much more laborious FE simulations.