You might look at this work by John Sullivan:
"[Discrete minimal surfaces in the cubic lattice](http://www3.math.tu-berlin.de/geometrie/ps/s_alt.shtml)," and his lecture on the topic [here](https://archive.org/details/lecture_10350):
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![Lattice Polyhedron][1]
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Incidentally, another version of the Schwartz $P$-surface is at [Alan Schoen's link](http://schoengeometry.com/e-tpms.html):
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![Schoen Polyhedron][2]


  [1]: https://i.sstatic.net/dqtX9.jpg
  [2]: https://i.sstatic.net/27G2k.jpg