Plotting the bifurcation surfaces in R^3.

{S6,S5,S2,S1,S3,S4,S8}

{-ch ((cg^2) (ch^2)+2 (cg^2) ch cl+8 (ch^3) cl+(cg^2) (cl^2)+12 (ch^2) (cl^2)+6 ch (cl^3)+(cl^4)-4 cg (ch^2) cm-2 cg ch cl cm+4 (ch^2) (cm^2)+4 ch cl (cm^2)+(cl^2) (cm^2)),(cg^2) (ch^2)+8 (ch^3) cl+2 (cg^3) cm-4 cg (ch^2) cm+18 cg ch cl cm-12 (cg^2) (cm^2)+4 (ch^2) (cm^2)-36 ch cl (cm^2)-27 (cl^2) (cm^2)+24 cg (cm^3)-16 (cm^4),(2 ch+cl) cm,-cm (-2 ch cl-(cl^2)+2 cg cm),ch (cg ch+cg cl+2 ch cm+cl cm),cl ((cg^2)+4 (ch^2)+4 ch cl+(cl^2)) (-cg ch+2 ch cm+cl cm),cg ch-cg cl-2 ch cm-cl cm}

{-ch ((cg^2) (ch^2)+2 (cg^2) ch cl+8 (ch^3) cl+(cg^2) (cl^2)+12 (ch^2) (cl^2)+6 ch (cl^3)+(cl^4)-4 cg (ch^2) cm-2 cg ch cl cm+4 (ch^2) (cm^2)+4 ch cl (cm^2)+(cl^2) (cm^2)),(cg^2) (ch^2)+8 (ch^3) cl+2 (cg^3) cm-4 cg (ch^2) cm+18 cg ch cl cm-12 (cg^2) (cm^2)+4 (ch^2) (cm^2)-36 ch cl (cm^2)-27 (cl^2) (cm^2)+24 cg (cm^3)-16 (cm^4),(2 ch+cl) cm,-cm (-2 ch cl-(cl^2)+2 cg cm),ch (cg ch+cg cl+2 ch cm+cl cm),cl ((cg^2)+4 (ch^2)+4 ch cl+(cl^2)) (-cg ch+2 ch cm+cl cm),cg ch-cg cl-2 ch cm-cl cm}/.{cm->1}

S3(GROC)

Show[ContourPlot3D[ch==0,{cl,-5,5},{cg,-5,5},{ch,-5,5},AxesLabel->{l,g,h},Mesh->None,ContourStyle->Directive[Yellow,Opacity[0.8],Specularity[White,30]]],ContourPlot3D[(2 ch+cg ch+cl+cg cl)==0,{cl,-5,5},{cg,-5,5},{ch,-5,5},AxesLabel->{l,g,h},Mesh->None,ContourStyle->Directive[Yellow,Opacity[0.8],Specularity[White,30]]]]

S2(VERD)

ContourPlot3D[2 ch+cl==0,{cl,-5,5},{cg,-5,5},{ch,-5,5},AxesLabel->{l,g,h},Mesh->None,ContourStyle->Directive[Green,Opacity[0.8],Specularity[White,30]]]

S1(BLAU FOSC)

ContourPlot3D[-2 cg+2 ch cl+(cl^2)==0,{cl,-5,5},{cg,-5,5},{ch,-5,5},AxesLabel->{l,g,h},Mesh->None,ContourStyle->Directive[Blue,Opacity[0.8],Specularity[White,30]]]

S5(VERMELL)

ContourPlot3D[-16+24 cg-12 (cg^2)+2 (cg^3)+4 (ch^2)-4 cg (ch^2)+(cg^2) (ch^2)-36 ch cl+18 cg ch cl+8 (ch^3) cl-27 (cl^2)==0,{cl,-5,5},{cg,-5,5},{ch,-5,5},AxesLabel->{l,g,h},Mesh->None,ContourStyle->Directive[Red,Opacity[0.8],Specularity[White,30]]]

S6(NEGRE)

Show[ContourPlot3D[(4 (ch^2)-4 cg (ch^2)+(cg^2) (ch^2)+4 ch cl-2 cg ch cl+2 (cg^2) ch cl+8 (ch^3) cl+(cl^2)+(cg^2) (cl^2)+12 (ch^2) (cl^2)+6 ch (cl^3)+(cl^4))==0,{cl,-5,5},{cg,-5,5},{ch,-5,5},AxesLabel->{l,g,h},Mesh->None,ContourStyle->Directive[Black,Opacity[0.8],Specularity[White,30]]],ContourPlot3D[-ch ==0,{cl,-5,5},{cg,-5,5},{ch,-5,5},AxesLabel->{l,g,h},Mesh->None,ContourStyle->Directive[Black,Opacity[0.8],Specularity[White,30]]]]

S8(BLAU CLAR)

ContourPlot3D[-2 ch+cg ch-cl-cg cl==0,{cl,-5,5},{cg,-5,5},{ch,-5,5},AxesLabel->{l,g,h},Mesh->None,ContourStyle->Directive[Cyan,Opacity[0.8],Specularity[White,30]]]

S4(LILA)

Show[ContourPlot3D[(2 ch-cg ch+cl) ==0,{cl,-5,5},{cg,-5,5},{ch,-5,5},AxesLabel->{l,g,h},Mesh->None,ContourStyle->Directive[Purple,Opacity[0.8],Specularity[White,30]]],ContourPlot3D[ ((cg^2)+4 (ch^2)+4 ch cl+(cl^2))==0,{cl,-5,5},{cg,-5,5},{ch,-5,5},AxesLabel->{l,g,h},Mesh->None,ContourStyle->Directive[Purple,Opacity[0.8],Specularity[White,30]]],ContourPlot3D[ cl==0,{cl,-5,5},{cg,-5,5},{ch,-5,5},AxesLabel->{l,g,h},Mesh->None,ContourStyle->Directive[Purple,Opacity[0.8],Specularity[White,30]]]]