Triangulations, Order Polytopes, and Generalized Snake Posets

Triangulations of Simplicial Polytopes

Various facts about triangulations of simplicial polytopes, particularly those pertaining to the equality case in the generalized lower bound conjecture, are collected together here. They include an apparently weaker restriction on the kind of triangulation which needs to be found, and an inductive argument which reduces the number of cases to be established.

Regular triangulations and resultant polytopes

We describe properties of the Resultant polytope of a given set of polynomial equations towards an outputsensitive algorithm for enumerating its vertices. In principle, one has to consider all regular fine mixed subdivisions of the Minkowski sum of the Newton polytopes of the given equations. By the Cayley trick, this is equivalent to computing all regular triangulations of another point set in...

Convex polytopes from nested posets

Motivated by the graph associahedron KG, a polytope whose face poset is based on connected subgraphs of G, we consider the notion of associativity and tubes on posets. This leads to a new family of simple convex polytopes obtained by iterated truncations. These generalize graph associahedra and nestohedra, even encompassing notions of nestings on CW-complexes. However, these poset associahedra ...

Inscribable polytopes via Delaunay triangulations

Enumerating Triangulations of Convex Polytopes

A triangulation of a finite point set A in IRd is a geometric simplicial complex which covers the convex hull of A and whose vertices are points of A. We study the graph of triangulations whose vertices represent the triangulations and whose edges represent geometric bistellar flips. The main result of this paper is that the graph of triangulations in three dimensions is connected when the poin...