work on surfaces via butterfly insertion

gap/PolygonalComplexes/discs.gi

@@ -133,3 +133,24 @@ end
 
 
 
+
+# Compute up to isomorphism all surfaces that can be obtained from
+# the surface surf by a butterfly insertion along a relevant 2-path
+
+InstallMethod( AllSimplicialSurfacesByEssentialButterflyInsertion,
+    "for a simplicial surface",
+    [IsSimplicialSurface],
+
+
+    function(surf)
+
+        local allp, surfaces;
+
+        allp := __SIMPLICIAL_AllEssentialTwoPaths(surf);
+
+        surfaces := List(allp, t-> ButterflyInsertionSurface(surf, t)[1]);
+
+
+        return IsomorphismRepresentatives(surfaces);
+
+end);

gap/PolygonalComplexes/modification.gd

@@ -1596,8 +1596,9 @@ DeclareOperation("SplitAllVertices", [IsPolygonalComplex]);
 #! Inserting a butterfly along the vertex-edge path
 #! @BeginExampleSession
 #! gap> disc := SimplicialUmbrella(5);
-#! gap> t:= [1,2,6];
-#! gap> discbig:=ButterflyInsertionSurface(disc,1);
+#! simplicial surface (6 vertices, 10 edges, and 5 faces)
+#! gap> t:= [1,2,6];;
+#! gap> discbig:=ButterflyInsertionSurface(disc,t)[1];
 #! simplicial surface (7 vertices, 13 edges, and 7 faces)
 #! gap> CounterOfVertices(discbig);  
 #! counter of vertices ([ 2, 3, 6 ] degrees, and [ 3, 3, 1 ] multiplicities)

gap/PolygonalComplexes/modification.gi

@@ -1892,9 +1892,6 @@ InstallMethod( ButterflyInsertionSurface,
         Length(CommonVerticesOfEdgesNC(surface,t[1],t[2])) = 0 then
           ErrorNoReturn("Requires a  pair of adjacent edges");
         fi;
-	if CommonFacesOfEdges(surface, t[1],t[2]) <> [] then
-          ErrorNoReturn("Edges cannot be incident to common face");
-       fi;
        t := Union(VerticesOfEdge(surface,t[1]),VerticesOfEdge(surface,t[2]));
        if not t[2]  in CommonVerticesOfEdgesNC(surface,t[1],t[2]) then
            w := t[2]; t[2] := t[1]; t[1] := w;
@@ -1905,10 +1902,6 @@ InstallMethod( ButterflyInsertionSurface,
        not IsVerticesAdjacent(surface, t[1], t[2] ) or
        not IsVerticesAdjacent(surface, t[2], t[3] ) then
         ErrorNoReturn("Requires vertex path of length 3");fi;
-       if Intersection(CommonFacesOfVertices(surface, t[1],t[2]),
-          CommonFacesOfVertices(surface, t[2],t[3])) <> [] then
-          ErrorNoReturn("Edges cannot be incident to common face");
-       fi;
     fi;