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Steiner Surfaces

Source Notebook

Classification of Steiner Surfaces

Originator: A. Coffman, A. J. Schwartz, C. Stanton

The representations of the real projective plane is called Steiner surfaces. A classification based on real parameters and transformations results in 10 types [1]. Two examples of Steiner surfaces include the Roman surface and the cross-cap [2].

(10 elements)

Examples

Basic Examples

An equation:

In[1]:=
ResourceData["Steiner Surfaces"]["8"]["Equation"]
Out[1]=

Visualize the surface:

In[2]:=
Module[{equation = ResourceData["Steiner Surfaces"]["8"]["Equation"], mr = 1, op = 0.9`, region = "sphere", r = 3.5`}, ContourPlot3D[Evaluate[equation], {x, -r, r}, {y, -r, r}, {z, -r, r}, Axes -> False, Mesh -> False, Boxed -> False, Background -> Black, MaxRecursion -> mr, BoundaryStyle -> None, ContourStyle -> Directive[Orange, Opacity[op], Specularity[White, 30]], RegionFunction -> Function[{x, y, z}, If[region == "cube", True, Norm[{x, y, z}] < r]], SphericalRegion -> True, PlotPoints -> 50]]
Out[3]=

Enrique Zeleny, "Steiner Surfaces" from the Wolfram Data Repository (2022)  

Data Resource History

  • Date Created:

Source Metadata

  • Source: http://users.pfw.edu/CoffmanA/steinersurface.html
  • Citation:
    • [1] A. Coffman, A. J. Schwartz, C. Stanton, "The algebra and geometry of Steiner and other quadratically parametrizable surfaces", Computer Aided Geometric Design 13, 1996 pp. 257-286.
    • [2] A. Coffman's page on Steiner Surfaces http://www.ipfw.edu/departments/coas/depts/math/coffman/steinersurface.html

Publisher Information

  • Prepared for the Wolfram Data Repository By: Enrique Zeleny
  • Publisher of Record: Enrique Zeleny