Symmetry can be widely found in natural phenomenon. Regular polygons and polyhedra are the most basic and important symmetrical structures in 2D and 3D Euclidean space. Four-dimensional regular polytopes (4-RPs) are the 4D analogs of regular polyhedra in three dimensions and regular polygons in two dimensions. After introducing the fundamental root systems of 4-RPs, this article presents three interesting methods to visualize 4-RPs using a fundamental region algorithm.