catenoid enneper3 grow 001
Catenoid-Enneper surface plotted with increasing range of the Enneer part. can be fitted together.

Catenoid-Enneper is created by fitting a Catenoid with Enneper Surface.

catenoid enneper5
Catenoid-Enneper with 5-fold symmetry
catenoid enneper8
Catenoid-Enneper with 8-fold symmetry
catenoid enneper12
Catenoid-Enneper with 12-fold symmetry
catenoid enneper20
Catenoid-Enneper with 20-fold symmetry
catenoid enneper40
Catenoid-Enneper with 40-fold symmetry
catenoid enneper st
catenoid enneper st
catenoid enneper sw
catenoid enneper sw

The surfaces Wavy Enneper, Catenoid Enneper, Planar Enneper, and Double Enneper are finite total curvature minimal immersions of the once or twice punctured sphere — shown with standard polar coordinates. These surfaces illustrate how the different types of ends can be combined in a simple way.

The pure Enneper surfaces (Gauss(z)=z^k, k=ee+1) and the Planar Enneper have been re-discovered many times, because the members of the associate family are CONGRUENT surfaces (as can be seen in an associate family morphing) and the Weierstrass integrals integrate to polynomial (respectively) rational immersions.

Double Enneper was one of the early examples in which I joined two classical surfaces by a handle.

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 Enneper

  1. Enneper Surface
  2. Double Enneper
  3. Planar Enneper
  4. Wavy Enneper
  5. Catenoid-Enneper

Related Surface of Catenoid

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