Category Archives: Projects

Overshadowed by the Packaging

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If companies wanted to be serious about getting even slightly more environmentally friendly (and save themselves money as well), they really ought to consider using less packaging. The amount of useless plastic being made just to securely package things in obnoxiously difficult to open clamshell packaging is rather mind-boggling.

Fortunately, sometimes that packaging doesn’t need to just get thrown out.

2012-07-02 18.55.05A couple years ago, shortly before people stopped selling them because of potential health risks to children, I bought a lot of those neat little magnetic ball toys. The packaging for these things was rather absurd. A large plastic box many times larger than the size of the balls contained within it. A few more plastic bits to keep everything held “just so” in the packaging. A small paper box with writing on it. And, of course, a small sturdy plastic box to store the magnetic balls in. It wasn’t just over-packaging. It was, over-over-packaging. And it made it rather hard to get at the part you wanted to play with too.

My friend Aviv Ovadya was over as I unpackaged them. As we fumbled with opening the packages, he proposed that we re-use some of the excessive packaging in math art (my friends are awesome like that).

I know Aviv through origami circles originally, and I think we both share a bit of the origami “aesthetic”. In particular, neither of us wanted to cut attachment holes or just glue the boxes together and be done with it. Fortunately, I happened to have a large package of rubber bands handy, so we experimented with different non-damaging ways of connecting the boxes using rubber bands, settling on creating a nice icosahedral structure with 30 boxes and 40 rubber bands.

If I’d made it more recently, I might have made a blog post about it then, but back then I rarely touched my blog, so that was the end of this particular diversion. The project might have been left undocumented forever, if I hadn’t realized a few weeks ago that the rubber bands holding it together had mostly disintegrated, and the structure needed to be trashed (boo!) or completely rebuilt. For the rebuild, I used small hair bands, which should last longer than regular rubber bands. The hair ties were also much more secure, so I only needed 20 of them.

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Probably the best thing about the transparent packaging material is how amazing the shadows through it look. Regular geometric objects often have cool shadow projections, but I think the ones here are particularly spectacular.IMG_0715

Do you have any packaging trash that could be transformed into something that might (like this) literally or figuratively overshadow the original packaging contents?

Hair Tie 120-cell

Image by Lucas Garron

About two years ago, I decided to make a 120-cell out of hair bands. I had just come back from Gathering for Gardner 10, where I had helped my friend Zach Abel build a cool, giant rubber band sculpture. This sculpture was fantastic and I loved how boingy it was. I was incredibly inspired by his idea and technique of using elastic bands to create geometric sculpture, and I wanted to try making my own.

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Shortly thereafter, Vi Hart asked me what my favorite polychoron was, a question to which I immediately answered “the 120-cell“.

See, my favorite number is five (a long-standing fact that first emerged when I was 5 years old), and, by extension, my favorite polygon is the five-sided pentagon. It naturally follows that my favorite polyhedron is the regular dodecahedron comprised of 12 regular pentagons. The 120-cell, made out of 120 regular dodecahedra, was basically a shoo-in for my favorite 4-polytope.

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Thus, when I discovered CVS selling colorful hair bands by the hundred, it seemed obvious that I needed to make a giant, bouncy (projection of a) 120-cell out of them. Hair bands seemed like a natural thing to use for a 120-cell. Their natural stretch means that you don’t need to get the lengths exact (just close), they come in all kinds of colors, and they have a truly delightful sproing to them which encourages people to really interact with the final sculpture.

I immediately purchased 600 hair bands (buying out the CVS in question), and got started. I particularly like the way that the Schlegal diagram of the 120-cell shows all of the edges and vertices and has a regular dodecahedron in the very center and one on the outside, so I knew that my 120-cell was going to use that projection and have 1200 edges, so this seemed like a good start. I assumed that I would be able to return to the store once I’d used up my hair ties and buy some more. Unfortunately, what I hadn’t account for was that CVS doesn’t actually restock that quickly. Moreover, since only the innermost edges of the sculpture were a single band length, and I was using a color scheme to keep track of my place in the sculpture, I was going to need way more than 1200 hair ties.

In desperation, I tried hair tie shopping at a different local store, but they didn’t have the same hair bands. I ended up buying out 5 or 6 CVS all across the Bay Area to finally end up with enough hair bands for my sculpture.

With the structure completed, I ran into a different issue. The sculpture was going to be huge and was going to need to be stretched out from multiple corners. It was probably going to fill a whole room, and I didn’t actually have a spare room handy. Fortunately, my boyfriend had a small extra bedroom in his apartment, and, one weekend we took a bunch of 3M command strips and attached it above the bed, which was awesome, but also a bit strange. This picture was carefully cropped to hide the bed.

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Not long thereafter we ended up taking the 120-cell down. Above one’s bed just isn’t a good permanent location, and the 120-cell languished in a bag for over a year before I had another opportunity to put it up in a small room in the CDG office.

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Did I mention that the 120-cell is rather large?

Check out this Youtube video to learn more about the hair tie 120-cell.

 

 

Polly wants a Parrotohedron

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Last week, I looked out the window of my office and saw a parrot. Two of them actually. Apparently San Francisco is home to a wild colony of escaped (released?) Cherry Headed Conures. There is even a documentary about them, but somehow I had seen nor heard of them before.

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I promise, these birds were parrots.

Walking back to my desk, I had a moment of inspiration.

Parrot. Pyrite. Pyritohedron.

I needed to make a Parrotohedron.

The internet is kind of amazing, and I quickly found a website that would sell me parrots in 3 different colors for 39 cents apiece. I think they are supposed to be used as accents for floral centerpieces; I have no idea how anyone is making a profit selling them at that price.

A parrotohedron obviously needs to be pyritohedral, so I started by arranging six sticks pyritohedrally for my parrots to perch on. Then, I arranged 12 parrots (one per stick end) such that each parrot had a friend (and represented one face of a pyritohedron).
parrot-gifSquawk! It’s a Polly-hedron.

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But will there be a pirate-ohedron? Only time will tell.

ps. Arrr. Where be my two-dimensional parrot?
pps. Polly gone.

Introducing the Tip Palindromator

It’s surprising to me how many people I know have independently taken to tipping such that the total is palindromic. The reasons for doing so are simple enough:

  1. It’s entertaining (for you and for the staff processing your charge)
  2. It helps you quickly verify credit card charges and check for potential fraudulence
  3. After a delicious sleepy meal late at night, one definitely needs to practice one’s mental math abilities…

Ok. We should probably strike #3.

  1. After a delicious sleepy meal late at night, one definitely needs to practice one’s mental math abilities…

The fact is we’ve all gotten checks where we definitely did not want to have to deal with figuring out precisely how much to tip. After one too many of those, I realized that I needed to create the Tip Palindromator (http://octahedralgroup.org/tip).

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The Tip Palindromator shows up great on mobile web. Want it as an application? Just choose the “add to home screen” option from your Android or iPhone web browser. The “Tip It” application is a great addition to the home screen.

It lets you quickly input your total bill and automatically finds a potential palindromic tip*, which can be adjusted up and down to find the perfect tip percentage.

Now, even the half-asleep can leave palindromic tips with ease.

* Note: I use this term to refer to a tip that leaves a total that is a palindrome, rather than a tip that is itself a palindrome.

Shortbraid and other geometric cookies

What happens when you combine three recreational math artists with a fantastic pastry chef?

Last weekend, Vi Hart, Gwen FisherRuth Fisher and I got together to try this experiment. Ruth provided several colors of shortbread dough and white chocolate “glue” and a few assorted cookie cutters. Gwen took photos (shown with permission below) and Vi took a bunch of video.

Our first idea was to make polyhedra cookies. The hexagon cookie cutter seemed to suggest truncated tetrahedra, octahedra, and icosahedra. We tried making one of each.

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Assembly was a bit tricky and required the use of an assortment of cardboard jigs to keep pieces in place while the chocolate dried.

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While our hexagon cookies were baking, Vi got started making a rhombic dodecahedron. We used a straight-edge to cut rhombi with the correct dimensions.

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She wanted to have little cut-out holes in her polyhedron, and used a rhombic cookie cutter that happened to have just the correct dimensions to tile the plane nicely.

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Which, of course, got us thinking about more interesting geometric tilings. For example, non-periodic Penrose tilings. Everyone likes the kite dart tiling and we made ourselves some cookie cutters out of card stock to generate kites and darts quickly.

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A real math cookie party isn’t complete with out some fractals (here we have some Sierpinski Tetrahedra)…

cookies10and some shortbread “shortbraids”. The three rings here form an 18-crossing Brunnian link.

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