gap> A1:= [ [1,2], [3,4], [5,6] ];;
gap> A2:=[ [1,2], [3,5], [4,6] ];;
gap> A3:=[ [1,4], [2,6], [3,5] ];;
gap> D8:=DihedralGroup(IsPermGroup,8);;

gap> NonManifolds:=[];;
gap> for A in [A1,A2,A3] do
> for x in D8 do
> for y in D8 do
> for z in D8 do
> G:=[x,y,z];
> F:=PoincareCubeCWComplex(A,G);
> b:=IsClosedManifold(F);
> if b=false then Add(NonManifolds,F); fi;
> od;od;od;od;

gap> D:=Classify(NonManifolds,inv3); #See above for inv3
gap> D:=List(D,x->x[1]);;
gap> Size(D);
367

gap> M:=List(D,ThreeManifoldWithBoundary);;
gap> C:=Classify(M,invariant1);; #See above for invariant1       
gap> List(C,Size);
[ 33, 13, 3, 18, 21, 7, 6, 13, 51, 2, 1, 15, 11, 11, 1, 35, 2, 2, 6, 15, 
  17, 2, 3, 2, 14, 17, 3, 1, 25, 8, 4, 1, 4 ]

gap> inv5:=function(m)                       
> local B;
> B:=BoundaryOfPureRegularCWComplex(m);;
> return invariant1(B);
> end;;

gap> CC:=RefineClassification(C,inv5);;
gap> List(CC,Size);
[ 25, 5, 3, 5, 4, 4, 2, 1, 11, 3, 4, 7, 3, 6, 4, 1, 5, 1, 1, 5, 1, 13, 4, 
  6, 40, 1, 2, 1, 11, 4, 5, 3, 1, 2, 7, 4, 1, 14, 11, 10, 2, 2, 6, 9, 3, 3, 
  2, 15, 2, 3, 2, 14, 17, 2, 1, 1, 4, 7, 14, 8, 3, 1, 1, 4 ]

gap> CC:=RefineClassification(CC,invariant2);;
gap> List(CC,Size);                              
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
  1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 3, 1, 1, 2, 1, 2, 1, 4, 2, 3, 2, 3, 
  4, 3, 2, 1, 1, 3, 2, 4, 3, 1, 1, 5, 1, 1, 3, 1, 1, 1, 13, 3, 1, 4, 2, 1, 
  2, 2, 3, 3, 3, 4, 4, 2, 4, 4, 4, 4, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
  1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
  1, 1, 1, 1, 2, 3, 4, 3, 1, 2, 3, 2, 3, 4, 3, 3, 2, 2, 1, 1, 2, 1, 1, 2, 
  1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 10, 5, 2, 3, 2, 14, 17, 1, 1, 1, 
  1, 4, 5, 2, 9, 1, 4, 7, 1, 3, 1, 1, 4 ]
gap> Length(CC);
180
