Classification of Simplex Sections Defined by a Hyperplane

In a number of applied problems [6]-[8] the points of the simplex are considered as states of some biological (physical, economic, etc.) system. The transition from one state to another is specified by an evolutionary operator, which can be a differential equation (with or without memory) or a difference equation. Depending on the parameters, the evolution of the system can occur only on some hyperplane intersecting the simplex [1]. In this case, the problem of determining the type of the resulting polyhedron arises.