Concave octahedron made from spherical segments
Sándor Kabai
A sphere of divided into eight identical parts. These spherical segments are moved in radial direction to create concave octahedron.
A sphere of divided into eight identical parts. These spherical segments are moved in radial direction to create concave octahedron.
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cp=ContourPlot3D[{x^2+y^2+z^21},{x,0,b},{y,0,b},{z,0,b},Mesh->None][[1]];cp1=Translate[cp,0.71{-1,-1,-1}];cp4=Table[Rotate[cp1,i2Pi/4,{0,0,1}],{i,4}];cp5=Rotate[cp4,Pi,{0,1,0}];Graphics3D[{cp5,cp4},Boxed->False,SphericalRegion->True]
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(*thesamewithmesh*)b=0.71;cp=ContourPlot3D[{x^2+y^2+z^21},{x,0,b},{y,0,b},{z,0,b},Mesh->20][[1]];cp1=Translate[cp,0.71{-1,-1,-1}];cp4=Table[Rotate[cp1,i2Pi/4,{0,0,1}],{i,4}];cp5=Rotate[cp4,Pi,{0,1,0}];Graphics3D[{cp5,cp4},Boxed->False,SphericalRegion->True]
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Manipulate[cp=ContourPlot3D[{x^2+y^2+z^21},{x,0,b},{y,0,b},{z,0,b},Mesh->None,BoundaryStyle->Black,ContourStyleFaceForm[Cyan,Yellow]][[1]];(*thisiswherethesegmentsaremovedtotheoppositeside*)cp1=Translate[cp,-{b,b,b}];cp4=Table[Rotate[cp1,i2Pi/4,{0,0,1}],{i,4}];cp5=Rotate[cp4,Pi,{0,1,0}];Graphics3D[{cp5,cp4},Boxed->False,SphericalRegion->True,ImageSize->400],{{b,0.8,"cut"},1,0.71},TrackedSymbols:>{b}]
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(*thesphereisshownasifcutbythefacesofacube*)Manipulate[cp=ContourPlot3D[{x^2+y^2+z^21},{x,0,b},{y,0,b},{z,0,b},Mesh->None,BoundaryStyle->Black,ContourStyleFaceForm[Cyan,Pink]][[1]];(*thisiswherethesegmentsarenotmovedtotheoppositeside*)cp1=Translate[cp,0{b,b,b}];cp4=Table[Rotate[cp1,i2Pi/4,{0,0,1}],{i,4}];cp5=Rotate[cp4,Pi,{0,1,0}];Graphics3D[{cp5,cp4},Boxed->False,SphericalRegion->True,ViewPoint->{100,100,100},ImageSize->400],{{b,0.8,"cut"},1,0.71},TrackedSymbols:>{b}]
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