Steiner Surface

Author

Eric W. Weisstein
June 10, 2008

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

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

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

Type 2

eqn=x^2y^2-x^2z^2+y^2z^2-x y z;

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

Plot

ContourPlot3D[eqn==0,{x,-2,2},{y,-2,2},{z,-2,2},MaxRecursion->4,RegionFunction->(#1^2+#2^2+#3^2<2^2&)]

Gaussian Curvature

SortBy[FullSimplify[GaussianCurvature[eqn,{x,y,z}]],ByteCount]

ByteCount/@%

Type 4

eqn=y^2-2x y^2-x z^2+x^2y^2+x^2z^2-z^4;

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

Plot

ContourPlot3D[eqn==0,{x,-2,2},{y,-2,2},{z,-2,2},MaxRecursion->4,RegionFunction->(#1^2+#2^2+#3^2<2^2&)]

Gaussian Curvature

SortBy[FullSimplify[GaussianCurvature[eqn,{x,y,z}]],ByteCount]

ByteCount/@%