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Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis.[1] For example, a baseball bat without trademark or other design, or a plain white tea saucer, looks the same if it is rotated by any angle about the line passing lengthwise through its center, so it is axially symmetric.

A surface of revolution has axial symmetry around an axis in 3-dimensions.

Axial symmetry can also be discrete with a fixed angle of rotation, 360°/n for n-fold symmetry.

Axiality (geometry)
Circular symmetry
Reflection symmetry
Rotational symmetry has a more general discussion
Chiral symmetry describes the use in quantum mechanics

References

"Axial symmetry" American Meteorological Society glossary of meteorology. Retrieved 2010-04-08.