The Kagome Lattice is one instance of a geometric structure called uniform tiling. Specifically, the Kagome Lattice is a type of trihexagonal tiling, where a repeated structure is made up of triangles and hexagons. I learned of it through a presentation at a meeting of the physics group I work for at Brandeis University. While I can't claim to know much about what physical systems this lattice represents or what special properties it has, I do know that it has a very interesting method of folding and I wanted to see it happen in real time.
This lattice prints entirely in place with no raft, no supports, and no assembly required. It works right off the build plate, which was a goal of mine that I'm thrilled to have achieved. Each connection site has ~120 degrees of rotational freedom. You can either scale down the STL or 3MF file I've included to fit your printer, or you can manually create a lattice of the size you want by translating the individual triangles to their appropriate spot using the "KagomePositive" and "KagomeNegative" files I've included.
I highly suggest using the "Horizontal Size Compensation" tool in the "Other" tab of the Simplify3D Process Settings. This will ensure that the connnection sites don't fuse and that you can rotate each triangle easily. I personally set it to -0.10mm compensation as any more would remove some of the mesh, but play around and see what works for your printer. Additionally, I used the "Scale to Maximum Size" tool in the Edit tab to easily get the lattice to fit the printer I used, and manually adjusted the z-axis height to my desired 3mm.
If scaling the lattice to maximum size for your printer causes the small details in the connection sites to be too small to print, you can either use the "Separate Connected Surfaces" tool in the Mesh tab to allow yourself to delete individual triangles to make the lattice smaller, or you can use the included "KagomePositive" and "KagomeNegative" files to construct your own ideal size lattice.
Give each individual connection site a bit of a twist to break any strings that might have formed mid-printing and you're done!
I used Autodesk Fusion360 to design the basic positive and negative pieces. Parametric CAD made this an incredibly easy process and I got to try out some new tools I hadn't used before like creating a new axis and patterning faces circularly about the center of an object.