This could be used as an infill for 3D printed parts.
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.
It comes from this paper:
"Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness".
The 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.
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.
Added a quicker rendering source files and
smaller models that print in a more reasonable time.
v1 was too big, v2 was too solid
Walls are 0.8mm in the (unscaled) model.
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.