Dynamic geometry software (DGS) has long been studied in mathematics education as a way for students to explore and interact with geometric objects and figures. Recent advances in Augmented Reality (AR) technologies that allow dynamic three-dimensional mathematical objects to appear in students' environment as holograms have changed the nature of what is possible for a DGS, particularly with respect to embodiment. New forms of embodied interactions may arise in AR-based DGS, as students gesture and move their bodies through their environment, taking different perspectives to interact with these immersive shapes projected in three dimensions. In the present study, we examine videos of 28 high school students interacting with an AR-based version of the DGS GeoGebra, while wearing the Microsoft HoloLens 2 headsets. We document the novel kinds of embodied interactions that the AR environment affords, relating to (1) perspective and orientation, (2) scale, (3) three dimensions. Based on our analysis, we give important directions for future research on DGS and implications for the design of the next generation of holographic DGS. [This paper was published in "Journal of Mathematical Behavior" v75 Article 101175 2024.]