A Schwarz H surface is a member of Schwarz's one-parameter family of embedded surfaces that are triply periodic minimal surfaces with hexagonal symmetry. The quotient space under its group of translational periods is a compact surface of genus 3 (Chen and Weber 2021).
A fundamental piece is obtained by solving Plateau's problem for two equilateral triangles
in parallel planes, forming opposite faces of a triangular
prism. Suitable half-turn rotations
extend it to the periodic surface. The triangles
are translates of each other, unlike the corresponding construction of the Schwarz
P surface, in which they are rotated by 
(Weber). The family has limits resembling parallel
planes joined by catenoidal
necks and a singly periodic minimal
surface whose translational quotient space
has six ends (Chen and Weber 2021).
