rotational symmetry
symmetry (something looking the same) under rotation
radial symmetry
arrangement of the body of an animal in which parts are arranged symmetrically around a central axis
axial symmetry
symmetry with respect to an axis, when a shape which does not change upon undergoing a rotation around its symmetry axis
spherical symmetry
symmetry with respect to a point, when a shape which does not change upon undergoing a rotation around its symmetry point