Humans and virtual agents (usually embodied in the physical world as physical robots) could coexist within the shared environment, which naturally creates a mixed reality environment of the physical and virtual worlds. In this paper, we analyze the characteristics of symmetrical reality with two different perception centers, and all of the mixed forms of physical and virtual reality can be treated as special cases of symmetrical reality. The experiment of folding clothes is implemented to demonstrate the significance of symmetrical reality for human-robot interaction, which also shows the general pipeline of building the symmetrical reality system with two minds (i.e., the human mind and agent mind) involved.