Cylindrical Symmetry

Symmetry of an Infinite Cylinder

An infinite cylinder is a paper towel roll or wooden dowel that goes on forever in both directions. It has a special type of symmetry as well, though its properties can't be summed up quite as neatly as for a sphere:

The symmetries of an infinite cylinder, or at least a picture of same
These properties are true for solid cylinders and cylindrical shells, which we say have infinite cylindrical symmetry. An infinite line (like the axis of an infinite cylinder) also has infinite cylindrical symmetry.