Infinite Polyhedra and Cubic Honeycombs in Beads

Here are a couple of beaded honeycombs.  In geometry, a honeycomb is a way to fill space with polyhedra, with no overlaps or gaps, like a tiling (tessellation), but in more than two dimensions.  A beaded honeycomb is a 3D weave of a honeycomb, where (a) beads are placed on every edge of the honeycomb and (b) two beads are connected if they are on adjacent edges of the same polygonal face in the honeycomb. First is this tetrahedral-octahedral honeycomb I beaded in 2006, and it's remained one of my favorite beaded beads since then.  Today, I finally got some better photos of it.

 At the time, I made this, I knew that it represented some sort of crystal structure, and I knew there were at least a couple hundred different molecular arrangements of crystals.  (In fact, there are 230 space groups.)  I was a little overwhelmed by the possibilities at the time. So I shelved the idea of looking at them until lately.   I recently beaded this bitruncated cubic honeycomb.

If you like this post, you'll certainly enjoy the beaded runcitruncated cubic honeycomb.  I like to imagine that I'll find time to bead more of these honeycombs in the future, now that we have Wikipedia as a resource.  If you have a favorite honeycomb that you want to see rendered in beads, let me know because I could really use some help picking.  There's just so, so many to choose from! Anyway, thanks for looking.