(* Two spheres of opposite index start to overlap, and the plotting goes rogue.  Starts self-dual, then loses that symmetry. *)

Clear[r]

n=4;

X={{0,1,0,0},{1,0,0,0},{0,0,r,1},{0,0,1,r}};

MatrixForm[X]

Y={{0,-I,0,0},{I,0,0,0},{0,0,0,I},{0,0,-I,0}};

MatrixForm[Y]

Z={{1,0,0,0},{0,-1,0,0},{0,0,1,0},{0,0,0,-1}};

MatrixForm[Z]

sigma1 = {{0,1}, {1,0}};

sigma2 = {{0,-I},{I,0}};

sigma3 = {{1,0},{0,-1}};

loclzr = KroneckerProduct[sigma1, X- x*IdentityMatrix[n]] + 
KroneckerProduct[sigma2,Y-y*IdentityMatrix[n]]+ 
KroneckerProduct[sigma3, Z-z*IdentityMatrix[n]] ;

charpoly = Det[loclzr];

step = 1/6;

plots=ParallelTable[ContourPlot3D[charpoly== 0, {x,-1.6,1.6}, {y,-1.6, 1.6}, {z, -1.6,1.6},Contours->{{1,LightBlue}},PlotPoints->100,ViewPoint->{4,-18,2}],{r,0,3/6,step}]

Export["ClassAIIsphere0_6.eps",plots[[1]],ImageSize->2.5*72];

Export["ClassAIIsphere1_6.eps",plots[[2]],ImageSize->2.5*72];

Export["ClassAIIsphere2_6.eps",plots[[3]],ImageSize->2.5*72];

Export["ClassAIIsphere3_6.eps",plots[[4]],ImageSize->2.5*72];