Alan Schoen’s R3 surface spans a minimal cylinder into the boundaries of the top and bottom faces of a right prism over a 30º-60º-90º triangle. It is thus a variation of his R2 surface (45º-45º-90º triangle) and the R1 surface (60º-60º-60º triangle), which is better known as the Schwarz H surface.

A translational fundamental piece consists of a third of the height of the hexagonal tower above. Limits are, as one expects from R1 and R2, of catenoidal and Scherk type:

The flat structures for G dh and 1/G dh are pretty, too, they provide a conformally flattened version of the minimal cylinders between the triangles:

Below is an animation of the entire family.

##### Resources

Mathematica Notebook

PoVRay Sources