stiffest possible infill

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".
https://www.nature.com/articles/nature21075
doi: 10.1038/nature21075

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.

Related discussion:
https://plus.google.com/+NicholasSeward/posts/hDYhP91YNph

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.

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