In a "problem of a week" contest in my school, I gave the following problem to students: we assign to each vertex of a cube a number $1$ or $-1$. And we associate to each face the product of the ...
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 ...
One of the interesting problems in abstract polytope theory is to determine, for a given finite group, when that group is the automorphism group of a regular abstract polytope. This is equivalent to ...