Tetrahedral honeycomb?
For designing your part, especially considering the repetitive mathematics involved, I would consider to learn to use OpenSCAD. I've learned the program and it fits your modeling requirement quite well. I feel it's easy to learn and is somewhat easier for folks who have a programming background. I don't have one, but it's still a logical progression to learn this program.

Regarding the SLS aspect, that also jumped out at me as a suitable answer. Solid shapes require to have "drain holes" to reduce the amount of powder consumed by the process.

I am assembling a Sintratec SLS printer and your model is the sort of thing I would enjoy to create with the printer. I've not yet listed my Sintratec printer on 3dhubs to solicit business, simply because it's not yet a fully assembled printer!

I did a quick Google search for "openscad tetrahedral honeycomb" and found this link:

http://forum.openscad.org/Beginner-Honeycomb-advice-needed-td4556.html

The result is more a polygonal honeycomb, not a true 3d tetrahedron, but it's a start. The file that created it is fewer than a few dozen lines of code.

The post is old  enough that the internal links no longer work but the OP posted his module code and that does work:



I'm not sure how personal contact works in stackexchange, but I'd be willing to work with you regarding creating your code and if the printer ever gets assembled, printing out your part.



Adding a picture again, to show the latest revision, based on the updated information: