Explain the combination relationship between different rotation operations of Pyraminx by using group theory, finding the solution sequence from the initial state to the target state

This article explores the strategy of combining group theory and programming methods to study and solve the problem of irregular Rubik’s Cube. Group theory, as an important branch of algebra, is a powerful tool for studying symmetry and structural transformations. In the study of Rubik’s Cube, group theory is widely used to analyze various transformations and their inherent mathematical properties. Irregular Rubik’s Cube, compared to traditional standard Rubik’s Cube, has a more complex structure and transformation mode, which requires us to consider more subgroups, quotient groups, and their nested relationships when applying group theory.