Shelling pseudopolyhedra

Abstract

The notion of shellability originated in the context of polyhedral complexes and combinatorial topology. An abstraction of this concept for graded posets (i.e., graded partially ordered sets) was recently introduced by Björner and Wachs first in the finite case [1] and then with Walker in the infinite case [11]. Many posets arising in combinatorics and in convex geometry were investigated and some proved to be shellable. A key achievement was the proof by Bruggesser and Mani that boundary complexes of convex polytopes are shellable [4]. We extend here the result of Bruggesser and Mani to polyhedral complexes arising as boundary complexes of more general convex sets, called pseudopolyhedra, with suitable asymptotic behavior. This includes a previous result on tilings of a Euclidean space ℝ d which are projections of the boundary of a (d+1)-pseudopolyhedron [7].