In 1990, Sven Lidin and Stefan Larsson found in the associate family of a particular member of the Schwarz H-surfaces a new embedded triply periodic minimal surface, similar in appearance to Alan Schoen‘s Gyroid. Below are corresponding pieces of the H surface, an intermediate member of the associate family, and the Lidinoid.

A much larger piece is shown in the stereo pair below:

There is strong numerical evidence (see Adam Weyhaupt’s paper) that the Gyroid can be deformed into the Lidinoid through embedded minimal surfaces that all have an order 3 rotational symmetry. It is not known whether either surface can be deformed (through embedded minimal surfaces) into any other known triply periodic minimal surface.

Resources

Mathematica Notebook

PoVRay Sources

A. Weyhaupt: Deformations of the Gyroid and Lidinoid Minimal Surfaces, Pacific Journal of Mathematics 235 (2008), 137–171.