Structural segmentation of music refers to the task of finding a symbolic representation of the organisation of a song, reducing the musical flow to a partition of non-overlapping segments. Under this definition, the musical structure may not be unique, and may even be ambiguous. One way to resolve that ambiguity is to see this task as a compression process, and to consider the musical structure as the optimization of a given compression criteria. In that viewpoint, C. Guichaoua developed a compression-driven model for retrieving the musical structure, based on the "System and Contrast" model, and on polytopes, which are extension of nhypercubes. We present this model, which we call "polytopic analysis of music", along with a new opensource dedicated toolbox called MusicOnPolytopes (in Python). This model is also extended to the use of the Tonnetz as a relation system. Structural segmentation experiments are conducted on the RWC Pop dataset. Results show improvements compared to the previous ones, presented by C. Guichaoua.