The edgeflip removes the common edge of two neighboured triangles
and replaces it by the connection of the opposite vertices. The edgeflip
must not be done if the common edge connects at least one vertex of degree 3.
Theorem 1 (V.Eberhard)
Each simple polyhedral type with N vertices can be obtained
by edgeflips from any simple polyhedral types with N vertices.
In other words: Let P be the set of all simple polyhedral types
with N vertices. If we connect two types by an edge if the second
type can be obtained by an edgeflip from the first one, and if K
denotes the set of all these connections, the graph is 1-connected.