I am reading:
A right cylinder with cross section $\Omega$ is a solid that is formed by translating $\Omega$ along a line, or _axis_, that is perpendicular to it.
So my understanding now is a cylinder is any solid that can be formed by translating a 2D shape straight along an axis.
So extrusion forms a "cylinder", regardless of shape? What do you call a "cylinder with a hole in it" (one whose cross sectional area shape has a hole in it)?