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An object is axisymmetric if it has an axis from which the object is the same in any direction, i.e., from any point on the axis, the object is identical in any direction perpendicular to that axis. A disk, a sphere or cylinder is axisymmetric but a cube is not. A noun phrase for the quality of being axisymmetric is circular symmetry.
Within astronomy, a galaxy, a circumstellar disk, ring systems such as Saturn's may be very close to axisymmetric or largely so or generally not. Planets and stars, being basically spherical are quite close. Minor planets such as asteroids vary. Axisymmetric models (generally 2D models) are often used for astronomical objects to make the modeling tractable, a common practice for modeling nearly-axisymmetric objects, also used as rough approximations for others.