Endless Variations on a Theme

[This is post #27 in a mini-blog-post series for NaBloPoMo 2015. Jump to the first2 previous, or next post.]

In the last few days we’ve singled out five subtle, independent tweaks to the initial Straws Thingy design. Why stop here, when there are so many other variations to consider?!

First, I wanted each of our 32 configurations to maintain maximal symmetry: within each variant, each straw is used in precisely the same way as each other straw, except possibly for color. For example, if we decided that some vertices should be woven one way and some the other way, then these vertices, and the straws meeting there, could be distinguished. Or if some connections are short-into-long while others are long-into-short, these too would be functionally different. I simply can’t abide such untidiness!

Furthermore, the colors themselves do maintain some symmetry: when we rotate the piece to look at a different straw (or face or edge or vertex…), the worst that happens is we permute the colors: everything that was yellow is now green, everything that was green is now blue, etc.

Second, I wanted the differences to be structural. We touched on another one in the instructions: cutting vs folding the straws for insertion.


While these are indeed different preparations, the resulting geometric arrangements of straws are identical, so learning to distinguish them didn’t feel as mathematically exciting.

Finally, these 32 pass the first glance test: even when looking at all 32 Straws Thingys from yesterday, it’s not immediately apparent that there are any differences at all! You have to ponder, discover—dare I say learn!—in order to appreciate their uniqueness.


I don’t mean to say that only these 32 variants are interesting; just that they fit well together as a set. Outside of these, there are endless variations, remixes, or redesigns that are worth exploring, and I can’t wait to see what you come up with! For example, how about other shapes? Maybe consider some of the other polypolyhedra, some of which even work with the same size straws![1]


How about those too-narrow Market Basket straws from earlier—are they secretly optimized for a different arrangement? What other possibilities can you think of?!


  1. …and a different scaffold. More on this soon. []

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