Tanglecube

Author

Eric W. Weisstein
May 23, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Surfaces/Tanglecube.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Tanglecube.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Equation

eqn= x^4 - 5*x^2 + y^4 - 5*y^2 + z^4 - 5*z^2 + 11.8

x^4 - 5*x^2 + y^4 - 5*y^2 + z^4 - 5*z^2 + 12

AlgebraicDegree[eqn,{x,y,z}]

POV-Ray

<<Utilities`POVray`

TraditionalForm[eqn ]

POVCoefficients[Tanglecube,{x,y,z}]

Graphic

V5

<<Extra`ImplicitPlot3D`

With[{r=3},
Show[Graphics3D[{EdgeForm[],ImplicitPlot3D[eqn,{x,-r,r},{y,-r,r},{z,-r,r},Mesh->False,PlotPoints->50,DisplayFunction->Identity][[1]]
},Boxed->False]
]
]//Timing

V6

With[{r=3.5},ContourPlot3D[ x^4 - 5*x^2 + y^4 - 5*y^2 + z^4 - 5*z^2 + 11.8==0,{x,-r,r},{y,-r,r},{z,-r,r},RegionFunction->(#1^2+#2^2+#3^2<r^2&),Boxed->False,Axes->False,Mesh->None]
]

With[{r=3.5},ContourPlot3D[ x^4 - 5*x^2 + y^4 - 5*y^2 + z^4 - 5*z^2 + 11.8==0,{x,-r,r},{y,-r,r},{z,-r,r},RegionFunction->(#1^2+#2^2+#3^2<r^2&),Boxed->False,Axes->False,Mesh->None,PlotPoints->30]
]

With[{r=3.5},ContourPlot3D[ x^4 - 5*x^2 + y^4 - 5*y^2 + z^4 - 5*z^2 +12==0,{x,-r,r},{y,-r,r},{z,-r,r},RegionFunction->(#1^2+#2^2+#3^2<r^2&),Boxed->False,Axes->False,Mesh->None,PlotPoints->30]
]