Scherk surface

They were the third non-trivial examples of minimal surfaces (the first two were the catenoid and helicoid).

Scherk surfaces arise in the study of certain limiting minimal surface problems and in the study of harmonic diffeomorphisms of hyperbolic space.

Scherk's first surface is asymptotic to two infinite families of parallel planes, orthogonal to each other, that meet near z = 0 in a checkerboard pattern of bridging arches.

Scherk's second surface looks globally like two orthogonal planes whose intersection consists of a sequence of tunnels in alternating directions.

Its intersections with horizontal planes consists of alternating hyperbolas.

[4][5] To minimize confusion it is useful to refer to it as Scherk's singly periodic surface or the Scherk-tower.

Animation of Scherk's first and second surface transforming into each other: they are members of the same associate family of minimal surfaces.
STL unit cell of the first Scherk surface
Five unit cells placed together
Scherk's second surface
STL unit cell of the second Scherk surface