4D Hypercube of Straws Thingys!

[This is post #25 in a mini-blog-post series for NaBloPoMo 2015. Jump to the first, previous, or next post.]

We’ve been accumulating lots of variant Straws Thingys, all subtly different, but all just as symmetrical as the others. We saw two ways of messing with the 5 macroscopic tetrahedra themselves, and then we zoomed into the molecular level and rearranged the 20 triangles that build these tetrahedra. Today, we finally venture to atomic scales and manipulate the 60 straws directly.

Let’s interrogate another scaffold feature. The arrows on the scaffold told us which way each straw should point: long end goes here, short end points this way. But what’s special about the arrows’ placement?


As with yesterday, there are two answers. Firstly, if you disregard the arrows and insert straws randomly (still following the dashed lines, of course), then the straws end up inconsistently oriented: you’ll get two long or two short ends trying to come together, when you actually need one of each.

But secondly, why not reverse all the arrows at once? Each straw gets turned around in place, so the triangles remain intact. This is a fine thing to do!

The difference is rather subtle (especially to photograph!), so here’s another way to see it: the location of the seam between successive straws. I’ve changed one straw from yellow to blue to highlight the effect:


In the original (left), the seam is neatly tucked away underneath another straw. After reversing straw orientation (right), the seam jumps outside the weave, a tad more visible. Only a tad. But for this reason (and only this reason), this arrow decision was deliberate, unlike the three prior differences where I broke ties arbitrarily.

Finally, as before, we can make this change on all 8 of our prior versions. This gives us 16 different Straws Thingys! Will it never end?! Will Target never run out of straws?!

16 different Straws Thingys along 4 binary axes: Left Cube / Right Cube: mirror.
Sixteen distinct Straws Thingys along 4 binary axes. Left Cube / Right Cube: mirror. Left/Right within cube: color swap. Up/Down: triangle weave. Front/Back: straw direction.

By the way, these 16 things are determined by 4 independent binary axes, so this is a four-dimensional hypercube of Straws Thingys!

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