Menagerie of polygons UPDATE

Now community wiki.  My new version of the question is: let's make a big list of classes of polygons.  We may be able to produce the most comprehensive list on the web, or in the literature. If there is community interest, after Jan 1st I will organize the information from all the answers into a post on the community blog.

ORIGINAL QUESTION BELOW


  Could you recommend a source, either in print or online, for a menagerie of polygons?  An extensive/exhaustive list of classes of polygon?


The Wikikpedia article on polygons provides a partial classification, but I would like something more complete.  Also, I am not concerned about how to name a 90-sided figure.  Rather, I am trying to find a list of classes that contain infinitely many figures each (examples: star polygon, isothetic polygon).  

For example: actual words for "looks like a spider," "would look like a football if it were smoothed out," and so on.

I've already checked The Geometry Junkyard and several pages of a Google search, but perhaps I didn't know what to look for.

Thanks very much.
I think(?) I [Joe O'Rourke] was the first to introduce monotone mountains, but perhaps I copied
that class from someone else.  It is a subclass of monotone polygons, with one of the
two chains that constitutes a monotone polygon a single segment.
I used it in the paper,
"Vertex pi-lights for monotone mountains,"
9th Canad. Conf. Comput. Geom., Aug. 1997, pp. 1-5.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

Joe Mitchell subsequently used this class of polygons in his abstract,
"Triangulating Monotone Mountains,"
AMS 345/CSE 355 (PDF link).