Kummer=(x^2+y^2+z^2-mu^2 w^2)^2-(3mu^2-1)(w-z-Sqrt[2]x)(w-z+Sqrt[2]x)(w+z+Sqrt[2]y)(w+z-Sqrt[2]y)/(3-mu^2)

% Kummer surface with  8 double points

K8 = Kummer/.{w->1, mu^2->1/9}

ContourPlot3D[K8==0, {x,-2,2},{y,-2,2}, {z,-2,2}, ContourStyle->Directive[Opacity[0.6],Orange], Mesh->None,Axes->None]

% Kummer surface with  16 double pooints, 4 at the infinity

K16with4=x^4+y^4+z^4-(y^2z^2+z^2x^2+x^2y^2)-x^2-y^2-z^2 + 1

ContourPlot3D[K16with4==0, {x,-2,2},{y,-2,2}, {z,-2,2}, ContourStyle->Directive[Opacity[0.6],Orange], Mesh->None,Axes->None]

Show[%65,Boxed->False]

% Kummer surface with  16 double pooints

K16=(x^2+y^2+z^2-mu^2 w^2)^2-(3mu^2-1)(w-z-Sqrt[2]x)(w-z+Sqrt[2]x)(w+z+Sqrt[2]y)(w+z-Sqrt[2]y)/(3-mu^2)/.{mu^2->Sqrt[2], w->1}

ContourPlot3D[K16==0, {x,-2,2},{y,-2,2}, {z,-2,2}, ContourStyle->Directive[Opacity[0.7],Orange], Mesh->None, Boxed->False,Axes->False, Background->Black]

K4D4=(x^2+y^2+z^2-mu^2 w^2)^2-(w-z-Sqrt[2]x)(w-z+Sqrt[2]x)(w+z+Sqrt[2]y)(w+z-Sqrt[2]y)/2/.{mu^2->3, w->1}

K4D4outside=(x^2+y^2+z^2-mu^2 w^2)^2+(w-z-Sqrt[2]x)(w-z+Sqrt[2]x)(w+z+Sqrt[2]y)(w+z-Sqrt[2]y)/2/.{mu^2->3, w->1}

ContourPlot3D[K4D4outside==0, {x,-3,3},{y,-3,3}, {z,-3,3}, ContourStyle->Directive[Opacity[0.7],Orange], Mesh->None, Axes->None]

Show[%38,Boxed->False]

ContourPlot3D[K4D4==0, {x,-3,3},{y,-3,3}, {z,-3,3}, ContourStyle->Directive[Opacity[0.7],Orange], Mesh->None, Axes->None]

Show[%31,Boxed->False]

K12A1 = (x^2+y^2+z^2-mu^2 w^2)^2-(w-z-Sqrt[2]x)(w-z+Sqrt[2]x)(w+z+Sqrt[2]y)(w+z-Sqrt[2]y)/2/.{mu^2->2, w->1}

ContourPlot3D[K12A1==0, {x,-1.5,1.5},{y,-1.5,1.5}, {z,-1.5,1.5}, ContourStyle->Directive[Opacity[0.7],Orange], Mesh->None, Axes->None]

Show[%44,Boxed->False]

K6A3 = (x^2+y^2+z^2-mu^2 w^2)^2+(w-z-Sqrt[2]x)(w-z+Sqrt[2]x)(w+z+Sqrt[2]y)(w+z-Sqrt[2]y)/8/.{mu^2->1, w->1}

ContourPlot3D[K6A3==0, {x,-1.5,1.5},{y,-1.5,1.5}, {z,-1.5,1.5}, ContourStyle->Directive[Opacity[0.7],Orange], Mesh->None,Axes->None]

Show[%54,Boxed->False]

Show[%17,Axes->False]

Show[%18,Boxed->False]

Bohemian dome

ParametricPlot3D[{Cos[u],Sin[u]+Cos[v],Sin[v]},{u,0,2π},{v,-π,π}, Axes->None,PlotStyle->Directive[Opacity[0.5],Orange],Mesh->None,Boxed->False]