Collapsing three-dimensional convex polyhedra

Abstract

If L is a subcomplex of a simplicial complex K, we say that L is obtained from K by an elementary simplical collapse if K − L consists of a simplex σ of some dimension d together with one ‘free’ face of σ, i.e. a face τ of dimension d − 1 which is a face of no other simplex of K except σ. Such a collapse is said to take place through σ from τ. If L can be obtained from K by a finite sequence of elementary simplicial collapses we say that K simplicially collapses (s-collapses) onto L, denoted by K ↘ LIf K is regarded as being embedded in some Euclidean space we shall for convenience of notation fail to distinguish between K and its underlying polyhedron.