2simplices:=
[[1,2,4], [2,4,8], [2,3,8], [3,8,9], [1,3,9], [1,4,9],
 [4,5,8], [5,6,8], [6,8,9], [6,7,9], [4,7,9], [4,5,7],
 [1,5,6], [1,2,6], [2,6,7], [2,3,7], [3,5,7], [1,3,5]];;
T:=RegularCWComplex(SimplicialComplex(2simplices));
D:=DiagonalApproximation(T);;
p:=D.projection;
P:=ChainMap(p);
Print(IsIsomorphismOfAbelianFpGroups(Homology(P,0)),"\n");
Print(IsIsomorphismOfAbelianFpGroups(Homology(P,1)),"\n");
Print(IsIsomorphismOfAbelianFpGroups(Homology(P,2)),"\n");
Print(Size(Source(p)),"\n");
Print(Size(Source(P)),"\n");
Print(Size(Target(p)),"\n");
Print(Size(Target(P)),"\n");
del:=D.inclusion;;
Del:=ChainMap(del);
Print( Size(Target(Del)),"\n");