Recently, I was introduced to a wonderful object constructed of sticks and elastics, called the hexastix. These mind boggling structures were last seen in a book called The Symmetries of Things by John H. Conway, Heidi Burgiel and Chaim Goodman-Strauss.
Naturally, I wanted to build some of my own, so here is a brief account of those escapades.
First I made the biggest hexastix I've seen. I keep looking hungrily at wooden doweling and bamboo though.
If you build your own, you'll observe that the inner cage of the above shape is approximately a rhombic dodecahedron. More on inner cages in a moment.
Hmm, better yet, why don't we just snip off the extra bits and reveal the rhombic dodecahedron inside.
Realizing that a bunch of sticks (I'm calling each set of parallel sticks a bunch so that hexastix have four bunches) can be used in more than one hexastix, I started another structure - slightly wilder this time. It still needs work (more sticks and nicer elastics, actually).
I was so excited by this time that I made a video about making them and colouring your own toothpicks (highly recommendable. both the video and the colouring of the toothpicks).
Wanting to take the torch on the road with my I made a little educational kit so that I could show people (at the bar, no less) how to build their own hexastix. I think I've educated about six so far. It's a great party trick if you are a quirky guy like me.
One of my more contemptuous bar pupils made rhombic bunches instead of hexagonal ones. I was shocked at first and didn't know what to make of them. Then I made one like that at home and discovered that it has a different cage! It appears to be an octahedron (thanks to Luis Goddyn for noticing the error) that has had two opposite vertices squashed together somewhat, and then two other opposing vertices sliced off (in a natural way), to reveal rhombuses. Hopefully a good drawing or computer rendition will be forthcoming from me (or you?).
Stay tuned because I have one more surprise that I hope to build and show here soon :)
update 1: In the interim, I made a Fatsostix. It's a very full hexastix.
update 2: Thousands of viewers are on the edge of their seats, waiting for the final Hexastix project as the Hexastix champion (I am championing them to you right now) brings us one step closer with ... a Hexastix in a jar! I call it a Jarofstix.