Steiner Surface

steiner surface grow 021
Steiner Surface

The Steiner surface is an image of the projective plane. It is given as a quadratic map from the sphere, mapping antipodal points to the same point in R^3.

steiner surface grow 001
The animation starts from a polar cap and shows larger and larger pieces of the surface.
steiner surf ellipse mo 001
The Steiner surface is covered by a family of ellipses. The ellipses are images of the meridians of the domain sphere. The band between neigboring ellipses is a moebius strip. The animation moves these Moebius strips over the surface.
steiner polardisk moebi 001
This animation shows latitude bands on the surface, starting from a polar disk and ending at the equatorial Moebius strip. The equator Moebius strip has self intersections and therefore does not look like usual Moebius strips.
steiner surf patch ana
Steiner surface (anaglyph). Initial parts of the coordinate axes lie on the surface. These segments end in 6 pinch point singularities.
steiner surf wire ana
Steiner surface (anaglyph wireframe)
      Steiner Surface  Parametric Equations

  x = (aa * aa / 2) * (sin(2 * u) * cos(v) * cos(v))
  y = (aa * aa / 2) * (sin(u) * sin(2 * v))
  z = (aa * aa / 2) * (cos(u) * sin(2 * v))

Related Surface

  1. Cross-Cap Surface
  2. Boy's Surface
  3. Boy's Surface (Bryant-Kusner)
  4. Steiner Surface

Cross-Cap.pdf