Symmetry was not actually invented. It was just defined after the observation of similarly figured and shaped objects in nature.
Sponges exhibit a type of symmetry known as asymmetry. Unlike many other animals, sponges do not have a defined shape or symmetry, as they can vary greatly in form and structure. Some sponges may exhibit a degree of radial symmetry, but overall, they lack the organized symmetry seen in more complex organisms.
Reflection symmetry, reflectional symmetry, line symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection
line symmetry, rotational symmetry, mirror symmetry &liner symmetry
Asymmetry, Radial Symmetry, and Bilateral symmetry.