To maximize the volume of a rectangular prism using a 120 cm by 80 cm sheet of metal, the optimal configuration is a cube, which yields the highest volume for a given surface area. However, since the requirement specifies that none of the faces can be square, this complicates the problem, as any deviation from a cube results in a lesser volume. The discussion explores various configurations, including dimensions that approach a cube, but ultimately concludes that there is no unique solution that meets the criteria while maximizing volume. The mathematical approach involves setting up equations based on the dimensions and using derivatives to find maximum volume, but the restriction against square faces limits the options significantly. Thus, while the maximum volume can be calculated, achieving it without square faces is not feasible.