Journey to the edge of chaos

For arbitrary simplices, it is shown that for a fixed volume, the maximum perimeter is achieved with sets of edges consisting of only two or three groups of edges of the same length. Analogues of the Euler and Roucher inequalities are found. The main results of the work were reported at the World Congress “Theory of Systems, Algebraic Biology, Artificial Intelligence: mathematical foundations and applications”, 23-30.06.2023 at the topological section.