This could eventually be used as an infill for 3D printed parts.
It would need conversion into gcode generation for slicers though.
Not my expertise.

The foam achieves the so called Hashin-Shtrikman upper bounds on isotropic elastic stiffness. There may be other foams that perform equally well but there provenly cannot be any foams that perform better.

It comes from this paper:
"Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness". https://www.nature.com/articles/nature21075
doi: 10.1038/nature21075
 

In simple terms

It is a superposition of 
– simple-cubic infill with an
– octahedral infill (octet truss with filled in faces) of halve the size.

A "cubic-octahedral" infill - so to say.
IIRC The paper mentions a trademarked brand-name for this.
 

Print Settings

The default orientation is here chosen such, that no planes are coplanar to the printbed.
This is on the cost of a bit of the symmetry of the whole block.

Set line-width to 0.4mm to make every (vertical) wall exactly two outlines.

Slanted walls get sliced diagonally and thus get wider, so you may want to set more than one outline. Also due to this effect the slanted walls form islands and cause loads of retractions, so you may want to turn off retraction if you don't want to stress test your printer in that regard.

An actual infill would not get sliced to get infill itself, so it would print much faster and nicer than this quick test.

Rafts: No
Supports: No
Resolution: layer-height as you wish
Infill: set ~100%
Notes: Walls are 0.8mm in the (unscaled) model.
 

Edit 2018-02-19:

Added a quicker rendering source files and
smaller models that print in a more reasonable time.
v1 was too big, v2 was too solid

Related discussion: 
https://plus.google.com/+NicholasSeward/posts/hDYhP91YNph
Sunsetted. Grrrr. Sorry for the loss. Stay wary and vigilant!

Category: 3D Printing Tests