Visualization of Cyclic, Dihedral, and Symmetric Groups

Group theory plays an important role in mathematics, providing a framework to understand symmetries and structures across various fields. This study explores visualization techniques for cyclic, dihedral, and symmetric groups. Visual tools such as Circle Representations and Cayley graphs are employed to illustrate and analyze group properties, including element orders, inverses, group operations, and subgroup structures. In the case of cyclic groups, in addition to Cayley graphs, the circle representation was also used to geometrically model the group structure. For more complex groups such as symmetric groups and dihedral groups , Cayley graphs were studied to understand how group generators relate to group elements and to visualize their structural symmetries and subgroup formations. While Cayley graphs for cyclic, dihedral,