What is Polytypichedrons

The transitions from regular and semi-regular polytopes of various dimensions to dual polytopes are considered in detail. It is shown that any deviation of polytopes from the correct forms leads, in their dual modifications, to new classes of polytopes. Polytopes dual to the products of polytopes form the class of polyincidental polytopes. Their images are given, and their composition is precisely indicated. For example, the polytope dual to the product of a decagon and a decagon contains 100 tetrahedra. All of them are listed by vertices in the dual polytope. Regularly faceted polytopes with a large number of different types of gonohedrons (polytypichedron and polytypictops) for dual transitions form a new class of polytopes with faces of irregular shape and, accordingly, a new type of gonohedron. This can be important in the analysis of chemical structures, often characterized by deviations from regular geometric shapes.