We previously observed students gesturing during a symmetry and group theory activity. This prompted additional interviews, wherein we attempted to understand the semiotic function of these gestures. We report here on the gestures that students used in this context to represent symmetry elements, symmetry operations, and other related ideas. In the process, we developed a scheme to code gestures in a systematic way that enables qualitative analysis and may lend itself to quantitative methods. This analysis leads to two observables: physical forms and motions enacted while representing or thinking about symmetry. These gestures are metaphorical and allow us to infer cognitive notions underlying the gesture as part of the student's reasoning, their communication, or both. Characterizing these gestures and associated notions offers the opportunity to add to our understanding of how gesture and other embodied representations can systematically support student learning in relation to spatial concepts and descriptions in chemistry. This characterization also has implications for instruction to support student learning about symmetry in inorganic chemistry.