This includes (half-)infinite cylinders (which may have holes drilled some
of the way down, parallel to their axis), at least some polygons such as
the rectangle and regular octogon, a "U" if made properly, and many other
weird shapes.

It generalizes to some higher-dimensional shapes. For higher-dimensional
cylinders, it selects generalizations which have a linear (2-dimensional,
rather than higher-dimensional linear manifold) axis.

It excludes spheres and tori, and many other shapes of rotation/revolution.

Thus, we may want to refine the definition.

Comment #2: Re: Pathologies

Curtis W Franks (Fri Mar 10 06:11:17 2017)

krtisfranks wrote: > Thus, we may want to refine the definition. The current definition is this: "x1 is a set of points/shape (of any number of dimensions) such that x1 is connected and there exists a line L such that for any line L' that is parallel to L, if L' has nonempty intersection with x1, then there exists exactly one subinterval (line segment, ray, or line) J of L' such that J has nonzero (Lebesgue) measure and any subset of L' which nonemptily intersects x1 is contained in J. An axially-perpendicular cross-section of x1 probably is necessary to specify x2. See also: slanu, fru'austumu."