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Convex polytopes are the convex hulls of a finite set of points in Euclidean spaces. They have rich combinatorial, arithmetic, and metrical theory, and are related to toric varieties and to linear programming
2
votes
"Database" of simplicial polytopes/spheres
I want to mention a couple of resources that I haven't seen anyone else put up:
The simpcomp GAP package includes a simplicial complex library. As I understand it, it includes Frank Lutz's list (an …
6
votes
Does every simplicial polytope have a topology-preserving contractible edge?
I brought this thread to the attention of Eran Nevo, who gave some more references, and pointed out that the answer to the converse of your question (2) is "no".
In his thesis, which I gave the arXiv …