Infinite Skew Polyhedron (4.4.4.8) W*8

I'm beading an infinite polyhedron, also called an infinite skew polyhedron.   This structure continues to be full of surprises. 

It is a patch of the infinite polyhedron (4.4.4.8), called that because every vertex is surrounded by 3 squares and an octagon.  I copied this picture below from Crystal Structures I: Patterns and Symmetry by M. O'Keeffe and B. G. Hyde, Figure 7.42 because it's precisely my inspiration for this piece of beadwork.  You can see it's made up of cubes and octahedral prisms.

I'm simply placing one seed bead on each edge of this structure.  Accordingly, I'm using cubic right angle weave to make this, with bits of prismatic weave.  Really, it's just a 3D edge-only angle weave where some of the loops have four beads and some have eight beads.  I also added little bicone crystals on both bases of each octahedral prism for sparkle and structure.

I think I first learned about infinite polyhedra (or at least the idea first sunk in), when I read this paper

Patterned Triply Periodic Polyhedra, by Douglas Dunham. 

Here are some action photos so you can see my process a bit.  Here's the first bit I beaded.

After I added a bit more, it looked like a little square crown.  I might modify this little guy to make a new pendant design.  I think it's got a lot of potential.  This is precisely what is shown in Figure 7.42 above.

And then it turned into this, but my thread ran out just before finishing the last crystal filled bit (i.e., octahedral prism) to make the whole thing look like a cube. It's the center front rightish that's missing, right where the big hole is.

And here is where it is right now (and the first photo).  I think I'm going to keep going because every time I add more, it surprises me and looks different.  Why stop now, right?

 

It's done.  You can see more here: http://gwenbeads.blogspot.com/2014/01/infinite-skew-polyedra-pendant-with-craw.html, and it's for sale here.  Thanks for looking.