The H”-R surface is one of the many triply periodic minimal surfaces described in Alan Schoen’s NASA report from 1970. Below are two different translational fundamental pieces of the same surface. The genus of the surface is 5.
The name derives as in most of Schoen’s surfaces from the skeletal graphs: Their horizontal layers consist of the tiling by regular hexagons and a tiling by 60º rhombi, respectively. In both cases consecutive layers are joined by vertical edges.
The surface come in a 1-parameter family that has a nodal limit on one side and singly periodic Scherk surfaces on the other side.
Below is a calming animation.