If you want to know how a space-frame looks like 
where all the struts run in the [111] directions (miller indices)
then here it is. 

Directions where the corners of two dual tetrahedra point to like so:
https://commons.wikimedia.org/wiki/File:Dual_compound_4_max.png
Source: https://en.wikipedia.org/wiki/Compound_of_two_tetrahedra

Also there 111 directions can be seen here in yellow:
https://www.printables.com/model/430598-truncated-rhombicuboctahedron-bead

Printing:

No serious overhangs. 
It's an easy print.

Category: Engineering