Symmetric 4-noid

symmetric 4noid 001
symmetric 4-noid

Symmetric 3-noid

symmetric 3noid
Symmetric 3-noid

Symmetric 5-noid

symmetric 5noid
symmetric 5-noid

Symmetric 6-noid

symmetric 6noid 001
Symmetric 6-noid
symmetric 6noid oblique 001
symmetric 6-noid oblique

Symmetric 8-Noid

symmetric 8noid 001
symmetric 8-noid

symmetric 4noid st
symmetric 4-noid st
symmetric 4noid sw
symmetric 4-noid sw

The Symmetric 4-noid and Skew 4-noid are parametrized by 4-punctured spheres; we use lines which extend polar coordinates around the punctures. Formulas are from [K2].

The intersection of the two families is the 4-noid from the Jorge-Meeks family of k-noids. These k-noids are the first finite total curvature immersions where the Weierstrass data were manufactured to fit a previously conceived qualitative global picture of the surfaces.

We suggest morphing the relative size of the opposite pairs of catenoid ends in the symmetric case and the angle between the catenoid ends in the skew case. The skew surface family goes from the Jorge-Meeks 4-noid to surfaces which look like two catenoids joined by a handle. This convinced David Hoffman that the idea of adding handles might be promising.

Formulas are taken from:

For a discussion of techniques for creating minimal surfaces with various qualitative features by appropriate choices of Weierstrass data, see:

Symmetric_kNoid.pdf