The image corresponds to a circular helicoid. It was first constructed by me in my PhD Thesis (see also this paper), and simultaneous and independently by William H. Meeks and Matthias Weber in this paper. The circular helicoid is a minimal surface in Euclidean 3-space generated by solving the Björling problem along a circle, with a unit normal rotating at a constant angular speed along this circle.  All figures in this page are by M. Weber and can be found in his Minimal Surface Museum.


Circular helicoids are complete minimal surfaces of finite total curvature with genus zero and two ends. Other than the catenoid, which corresponds to the case where the unit normal is constant, they are never embedded.

When the number of twists of the unit normal along the circle is a half-integer, we obtain a minimal Möbius strip. They still define complete minimal surfaces of finite total curvature.