# File Geodesic_SketchUp.rb, line 147
        def self.expand_face( face, frequency, radius, entities )
                if frequency < 1
                        entities.add_face(
                                face.collect{ |v|
                                        v.normalize.scale_by( radius ).to_point3d
                                }
                        )
                else
                        a,b,c = face
                        ab = a + (b-a).scale_by( 0.5 ) 
                        ac = a + (c-a).scale_by( 0.5 )
                        bc = b + (c-b).scale_by( 0.5 )
                        [
                                [ a,  ab, ac ],
                                [ b,  bc, ab ],
                                [ c,  ac, bc ],
                                [ ab, bc, ac ]
                        ].each{ |f|
                                self.expand_face( f, frequency-1, radius, entities )
                        }
                end
        end