Slice of Menger sponge
Menger Sponge diagonally through the center? well, a very interesting pattern of stars and hexagons. This is the level four iteration on the Menger sponge.
I haven't seen this mentioned before on the internet. Maybe a reader will know if these intersections of the Menger Sponge have been studied before? Wolfram mentions that:
The Menger sponge, in addition to being a fractal, is also a super-object for all compact one-dimensional objects, i.e., the topological equivalent of all one-dimensional objects can be found in a Menger sponge (Peitgen et al. 1992).