A tale of centrally symmetric polytopes and spheres (Q2417466)

This paper is a nice survey on recent developments referring to the face numbers of centrally symmetric simplicial polytopes and spheres. Also various interesting open problems are presented, and the variety of discussed topics ranges from neighborliness of centrally symmetric polytopes and the upper bound theorem for centrally symmetric simplicial spheres to the generalized lower bound theorem for centrally symmetric simplicial polytopes and the lower bound conjecture for centrally symmetric simplicial spheres and manifolds. Each section contains interesting and deep research problems, and four deep conjectures are also posed. The paper is excellently written and gives a nice update of this interesting partial field of polytope theory. For the entire collection see [Zbl 1410.05001].