This paper presents some examples of symmetry and asymmetry in the geometry of 3D digital character, as well as in its movement. This is one of the topics studied in the Computer Graphics studies, which have existed for 11 years at the Faculty of Technical Sciences at the Uni- versity in Novi Sad. The first goal of this paper is to show how to create a 3D digital character, which consists of a surface called Mesh that connects to a system that allows the movement of that character, and that the system consists of a bone system with associated controls and is called a rig. The character is most often created using symmetry, namely, a mesh of one half of the character is created and then the other half of the character is obtained by creating a symmetrical half, and the plane of symmetry is a vertical plane that halves the character. The second goal is to show that the 3D character created in this way can be geometrically symmetric or asymmetric. The next goal is to show how symmetric or asymmetric character creates body movement or facial expression. The main goal is to emphasize the need to use asymmetric characters in 3D animation, as well as the motive for this, which emphasizes the fact that ideal symmetry in humans does not actually exist. Also, asymmetry gives us far more opportunities to create interesting differences in 3D characters.