Catenoid Fence

catenoid fence grow 001
catenoid fence grow
catenoid fence2 001
Catenoid Fence. This minimal family was suggested by the Skew 4-noid family. These are the first minimal surfaces with a designed handle.
catenoid fence st
catenoid fence st
catenoid fence sw
catenoid fence sw

These singly periodic surfaces are parametrized (aa) by rectangular tori; our lines extend polar coordinates around the two punctures to the whole Torus. The surfaces look like a fence of catenoids, joined by handles; they were made by Karcher and Hoffman, responding to the suggestive skew 4-noids. The morphing parameter aa is the modulus (a function of the length ratio) of the rectangular Torus.

Formulas are taken from:

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

Related Surface of Catenoid

  1. Catenoid
  2. Helicoid-Catenoid
  3. Catenoid-Enneper
  4. Catenoid Fence

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