A sphere has three types of geometrical symmetry: radial symmetry, rotational symmetry, and translational symmetry. Radial symmetry means that if you were to draw a line from the center of the sphere to any point on its surface, it would look the same as any other line drawn from the center to a point on the surface. Rotational symmetry means that the sphere looks the same no matter how it's rotated around its center. Translational symmetry means that the sphere looks the same no matter where it's located in space.