This paper explores the theory and practical aspects of the chase-escape game on the edges of regular polynomials. These games are usually studied in combinatorial game theory and graph theory, where the 'chaser' and 'escaper' move along the edges of the polyhedron, trying to catch or escape each other. The main principles, strategies and mathematical models describing these interactions are extensively covered in the article. Examples involving different types of regular polynomials are also considered, and general strategies and results are analyzed. This work is intended for researchers and students of mathematical and computer science interested in game theory, geometric models, and strategic problem solving.