5
votes
1answer
262 views

Does every simplicial polytope have a topology-preserving contractible edge?

An edge of a triangulated manifold is said to be contractible if it may be contracted to a vertex without modifying the topological type of the underlying manifold. Otherwise, the edge is ...
3
votes
0answers
146 views

What's the best way to test if a sphere is a polytope? (algorithms for the Simplicial Steinitz Problem)

The problem of recognizing whether a simplicial face lattice is polytopal is sometimes called the Steinitz problem. Sturmfels and Bokowski advanced a set of methods in the late 80s to test whether ...
13
votes
3answers
606 views

Triangulations of polyhedra

A topologist came to me with this question, but everything I think should work doesn't. How many triangulations are there of a polyhedron with n vertices? By a "triangulation" of a polyhedron P we ...