Boy’s Surface (Bryant-Kusner Parametrization) - new version: POV-Ray 3.6.1, 6/20/06
old version: Mathematica 4.2, MathGL3d, POV-Ray 3.6.1, 5/24/05
This one-sided surface was first parametrized correctly by Bernard Morin. The animation looks like it’s turning inside-out, although technically that’s impossible because it only has one side! Robert Bryant told me that the parameters (p,q) = (0,1) give this Willmore immersion of RP2 a trilateral symmetry. The parameters (p,q) = (1,0) should give bilateral symmetry. Click here to download some POV-Ray code for this image. |
Clifford Torus - Mathematica 4.2, POV-Ray 3.6.1, 8/12/08
The Hopf map is a special transformation invented by Heinz Hopf that maps to each point on the ordinary 3D sphere from a unique circle of points on the 4D sphere |
Inside the Flat (Euclidean) Dodecahedron - POV-Ray 3.6.1, 2/12/07
  Here is a dodecahedron viewed from the inside with flat mirrored walls.
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This 3D vortex image is hidden in the above pictur |
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