Ordering of convex polyhedra and the Fedorov algorithm

Abstract

A method of naming any convex polyhedron by a numerical code arising from the adjacency matrix of its edge graph has been previously suggested. A polyhedron can be built using its name. Classes of convexn-acra (i.e.n-vertex polyhedra) are strictly (without overlapping) ordered by their names. In this paper the relationship between the Fedorov algorithm to generate the whole combinatorial variety of convex polyhedra and the above ordering is described. The convexn-acra are weakly ordered by the maximum extra valencies of their vertices. Thus, non-simplen-acra follow the simple ones for anyn.