Step 7: Straws in Spaaace!

… three-dimensional space, to be precise.

[This is post #15 in a mini-blog-post series for NaBloPoMo 2015. Jump to the first, previous, or next post.]

Now that the scaffold is complete, let’s use it! Find your straws; today we’ll use just one of the five colors. Make sure they are already cut or creased as described in Step 1 few days ago.

To insert a straw into the scaffold: the long end of the straw enters at an arrow,

and it tracks the dotted gray line, emerging only when this line ends:

This is important: each and every straw will be inserted with this same recipe, and you don’t want them in backwards, so here are those steps again:

Insert the long straw end at an arrow, and follow the dotted line to the exit.

Let’s do the same to the other two arrows on the same hexagonal face:

Now there are four faces touching these three straws: the one whose arrows we entered with, and the three we exited from. The pink straws will touch only these four faces! So all that’s left to do is repeat with these other three. Here I’m using three more arrows on a second face (before and after):

And here’s the result with all 12 straws inserted into all 4 faces:

Tomorrow we’ll close up the corners to finish our first tetrahedron!

Step 6: Pentagons Galore

[This is post #14 in a mini-blog-post series for NaBloPoMo 2015. Jump to the first or previous, or next post.]

Three Dee, guys! We’re so close I can taste it! (tastes like paper…)

Take five of your finished scaffold units and lay them out in a star like this.

We’re going to staple the tabs together in pairs, to create a 5-sided hole in the center. Here’s the first staple:

And here are the other 4:

It won’t lie flat, and that’s exactly what we want! Lather, rinse, repeat with the other 5:

These are two halves of a sphere that we’re now going to join together. Form another pentagonal hole by stapling one scaffold unit from one half (bottom) between two other scaffold units from the other half (top):

All that’s left is some good old-fashioned pentagon hunting. Any time you see a five-sided hole that looks like it wants to close up, help it along! When you’re done, you should be staring at a soccer ball:

And that’s the finished scaffold! Great job!

Time to Build At Last! Step 1

[This is post #8 in a mini-blog-post series for NaBloPoMo 2015. Jump to the first, previous, or next post.]

It’s finally time to start building! By the end of this week you’ll have your very own Straws Thingy to keep you company. If you haven’t yet acquired your Target (or other carefully measured [see the previous few posts for details]) straws, now’s the time!

Let’s begin with a simple but immensely helpful step: grab some scissors and cut your straws lengthwise. No, not all the way! Just one slit on the short straw end, and just up to (but not including!) the flexy bits.

This will make it much easier to slide each straw into the next one in future steps. You’ll want to prep 12 straws in each of 5 colors, or 60 straws in all.

If you want to bring some origami back into the project, you can instead make a shallow crease, like this:

Either way, remember that the flexy bits will be visible in the final piece, so avoid cutting or creasing into them.

Oh, the Places You(r Straws Thingy)’ll Go!

[This is post #7 in a mini-blog-post series for NaBloPoMo 2015. Jump to the first, previous, or next post.]

OK! We’ve explored the geometry of Straws Thingy a bit, and we’ll do more of this later. But I think the rest of our mathematical discussion will be much more engaging with a Straws Thingy of your own in your hands!

So let’s start talking about how you can make your own, step by careful step. What’ll you do with yours?!

Blowing Up Straws

[This is post #6 in a mini-blog-post series for NaBloPoMo 2015. Jump to the first, previous, or next post.]

So how could we compute/visualize the “perfect” length to diameter ration? Let’s start with a smaller, simpler thingy made of straws (not to be confused with Straws Thingy itself):

And here’s finding the tight, optimal packing:

The tubes are inflating (or equivalently, shortening) while pushing away from each other. When they can’t inflate(shrink) any more, we’ve reached the ideal, tight packing.

We can do the same for Straws Thingy proper (it’s a bit more difficult to see, hence the example above):

The resulting tight packing has a length to diameter ratio of about 27.43, according to my Mathematica simulation. Why does this look so different from the 23 and change from yesterday? They are measuring slightly different things:

The 27.43 refers to the edge length of the “axial” equilateral triangle, whereas the straws “shortcut” these corners via flexy bits. Of course, the exact shortcut dimensions vary from brand to brand, which further explains why I didn’t offer more precision to yesterday’s 23-or-24 measurement.

OK! It’s time to switch focus away from discussing Straws Thingy‘s geometry and toward learning, step by step, how to make your own! So go out, find those straws, and get ready for some excitement!

No Target? No Problem

[This is post #5 in a mini-blog-post series for NaBloPoMo 2015. Jump to the first, previous, or next post.]

Sjoerd Visscher asked a great question on yesterday’s post: what to do if you can’t get this specific brand of straws? (Or, extrapolating, if you want a different color palette? Or just generally like doing things the hard way?) Thankfully, this is no problem. Comparing the long end of the straw (not including the flexy bits) to the diameter, you’ll want a ratio between 23 and 24. (This needn’t be too too precise. I’ve had success even at a 25-to-1 ratio—it felt only a tad loose.)

Measuring directly is certainly an option, especially if you have easy access to some calipers, but for a lower-tech solution, just line ’em up! These straws below are perfect, at 23 and change.

Keep in mind that there will be some manufacturing variation (these are not precision-critical parts in their intended use, after all!), so don’t worry too much about getting the absolute perfect ratio, or measuring each straw overly carefully.

So practically speaking, if you buy straws that are too long, cut to size. And if they’re too short, just leave them sticking out a bit:

But where does this “perfect” 23ish ratio come from? How might we compute it, without resorting to trial and error? We’ll talk about this tomorrow.

Straw Size Matters

[This is post #4 in a mini-blog-post series for NaBloPoMo 2015. Jump to the first, previous, or next post.]

Two days ago, I recommended Target’s up&up brand of flexible straws. Why so specific? Is Target sponsoring these posts? In a word: no. (Hint hint, Target! =D) So why these in particular?

For this model, the size of the straws is critical—specifically, the length-to-diameter ratio. If the straws you use are too long/skinny (like the ones below from Market Basket), the finished model turns out wobbly and unsteady, as if it (appropriately!) drank a bit too much.

On the other hand, use straws that are too short/fat and they simply can’t squeeze past each other. If you find those perfect Goldilocks straws—not too long, not too short, but just right—they keep Straws Thingy perfectly snug and sturdy. And in this regard, Target’s up&up straws hit a bulls-eye.

The Shape of Thingys To Come

[This is post #3 in a mini-blog-post series for NaBloPoMo 2015. Jump to the first, previous, or next post.]

OK, so what is this shape? As a first approximation, Straws Thingy is simply the Compound of Five Tetrahedra, a favorite among origami folders thanks to Tom Hull’s popular and supremely elegant design.

But on closer inspection, these tetrahedra break down into even smaller parts: each tetrahedron is made from four interwoven triangles, making 20 triangles in all. Here’s one such tetrahedron (left) with one of the four triangles distinguished (right):

Robert Lang describes this shape as a “polypolyhedron” (specifically, it is the mirror image of Polypolyhedron 44), and he originally classified all such shapes (there are 54) for origami—his folding of this particular polypolyhedron, a model he named K2, is especially stunning and took a full day to assemble!

I therefore like to think of Straws Thingy as origami without the origami. The straws’ flexy bits (technical term, I’m sure) do the folding for us, and instead of holding everything together with creases, we stick straws inside each other—the same beloved trick for blowing bubbles in my chocolate milk from across the room…

Enter Straws Thingy

[This is post #2 in a mini-blog-post series for NaBloPoMo 2015. Jump to the first or next post.]

Without any ado whatsoever (other than yesterday’s post, and now this sentence, and now this parenthetical, and now…), here’s a pretty thingy made of 60 drinking straws:

After much deliberation and Simple English Wikipedia browsing, I decided to call it Straws Thingy.

So what is it? How does it work? What is it good for? Why does it induce vertigo if you stare at it too long? And how can you make one yourself?

I’ll cover all this and more in the coming weeks. (Except for that 4th question. You might want to ask your doctor about that one). And yes, I’m confident that you can indeed make your own. To start, I suggest heading to Target and picking up a box of up&up 5-color flexible straws, making sure you have at least 12 of each color.