Reading through various papers on polytopes I have come across really interesting examples of simplical polytopes and non-shellable (or non-PL) simplicial spheres but sometimes it is hard to keep track of their provenance. The nice thing about the simplicial case is that in order to get the whole combinatorial structure all one needs is the list of the facets. My question:
Are there any "comprehensive" resources for examples of simplicial polytopes or spheres?
Here by comprehensive I mean either examples obtained via some construction method or an aggregate of various results in the field. These examples could come in any form I guess, but a simple list of facets would probably be the easiest to work with.
I've been searching around a bit and found the following sources:
John Palmieri gives an implementation in Sage of a few interesting examples of nonshellable spheres and manifolds here.
Frank Lutz gives examples of small non-constructible spheres here and he also has a few papers enumerating $3$-manifolds with $10$ vertices here and vertex-transitive triangulations (with E. Köhler) here. Although in the latter $2$ papers the facet-lists are not given.
I am sure there are many other papers that give examples of various interesting triangulations that I am not aware of so even if you do not know of a database of such examples, answering with specific papers would be useful, I think.