If the Schwarz P-surface is square based and the H-surface triangle based, Alan Schoen’s H’-T ( Hexagon-Triangle) surface from 1970 is based on a regular hexagon.

And, like these classical surfaces of Schwarz, it comes in a 1-parameter family that maintains its dihedral symmetries about a vertical axis, with a nodal limit and a Scherk limit.

The latter shows Alan Schoen’s reasoning for the name, because the two complementary regions have skeletal graphs based on a hexagon and a triangle, respectively. This also highlights a difference to P and H: The complementary regions are not congruent, as is the case for P, H, and in fact for any embedded genus 3 triply periodic minimal surface. H’-T has genus 4.

Two views of an intermediate member of this family are shown below.

Resources

Mathematica Notebook and CDF

PoVRay Sources