The alternating sign matrix polytope.
The angle defect for arbitrary polyhedra.
The cd-index of Bruhat intervals.
The Lower and Upper Bound Problems for Cubical Polytopes.
The Mayer-Vietoris and IC Equations for Convex Polytopes.
The minimal perimeter for confined deformable bubbles of equal area.
The skeleta of convex bodies
The connectivity and measure theoretic properties of the skeleta of convex bodies in Euclidean space are discussed, together with some long standing problems and recent results.
The upper bound conjecture for arrangements of halfspaces.
Triangulations of simplicial polytopes.