Eight circles of the sphere
Sándor Kabai
Eight great circles are aligned in parallel with the faces of two tetrahedra (stella octangula) and the vertices of a cube.
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r=0.5/Sin[2Pi/6];​​tor=Torus[{r,r+0.03}];​​tv=Table[r{Sin[i2Pi/3],Cos[i2Pi/3],0},{i,3}];​​tri=Polygon[tv];​​t1=Rotate[Translate[{tri,Yellow,tor},{0,r/2,0}],-Pi/2+ArcSec[3]/2,{1,0,0}];​​Graphics3D[{t1},BoxedFalse,SphericalRegionTrue,ImageSize300,ViewPoint->{0,0,100}]
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t2=Rotate[t1,Pi,{0,0,1}];​​t3=Translate[{t1,t2},{0,0,1/Sqrt[2]/2}];​​t4=Rotate[Rotate[t3,Pi,{1,0,0}],Pi/2,{0,0,1}];​​tet1={t3,t4};​​Graphics3D[{tet1},BoxedFalse,SphericalRegionTrue,ImageSize300,ViewPoint->{0,0,100}]
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tet2=Rotate[tet1,Pi,{1,0,0}];​​Graphics3D[{Pink,tet1,Cyan,tet2},BoxedFalse,SphericalRegionTrue,ImageSize400,ViewPoint->{0,0,100}]
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cub=PolyhedronData["Cube","Faces"];​​cubv=cub[[1]];​​cubn=Rotate[Scale[cub,0.68],Pi/4,{0,0,1}];​​spc=Sphere[{0,0,0},0.05];​​spcub=Rotate[Map[Translate[spc,#]&,0.7cubv],Pi/4,{0,0,1}];​​Graphics3D[{tet1,tet2,Red,spcub,Green,cubn},BoxedFalse,SphericalRegionTrue,ImageSize400,ViewPoint->{0,0,100}]
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sp=Sphere[{0,0,0},0.62];​​Graphics3D[{spcub,sp,Green,cubn,tet1,tet2},BoxedFalse,SphericalRegionTrue,ImageSize400,ViewPoint->{0,0,100}]
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