After Cory Poole posted some great Escher snowflakes, and Cerek Tunca had the great idea of using it as a base for a tetrahedron, well, I just had to give it a go. I will post a few more pictures and variants later (I think this was what Cerek was envisaging—if not let me know!)
Here's a Math Craft project that takes less than 20 minutes, has an attractive, practical result, and is at least a little mind-blowing due to folding along curves.
After becoming addicted to basic sonobe modular origami, I decided to make ornaments for relatives as Christmas gifts. I tried using fancy paper from stores like Paper Source, and cutting it to proper origami size, but I could never get the tight folds I wanted with non-traditional, non-origami paper. I ended up using this metallic origami paper that folds beautifully, and I'm pretty happy with the tiny models I ended up with. Forgive these pictures (iPhone/Instagram), I don't have my regular...
This is a zigzag tensegrity based on a small stellated dodecahedron. There are string pentagons on the outside of the model where the vertices have opened. It is made of thirty units, consisting of a barbecue stick pair with a loop of elastic. The stick pairs are all "floating", and weave through the model without contacting any other stick pairs. It is quite tricky to assemble, but can be done entirely by hand.
My first attempt with the sonobe unit! I'm now addicted. I'll be spending the holiday folding. Instructions here.
I wish there was more information about this impressively massive sonobe model, but all I can glean is that it appears to have been made by Imogen Warren, and was posted by Room 3. So awesome.
Tom Friedman is one of my favorite artists. He's got a great sense of humor, and his work is meticulous and beautiful. He forays into Math Art, and from a partisan perspective, he seems to be inspired by mathematics, but the end results are more of a whimsical twist than a mathematically "correct" execution. But I could be totally wrong. Comment below and fill me in.
Here's my version of his icosahedron: I colored it in this one so that you can see the pentagonal faces of a dodecahedron:
These drawings were made with Google SketchUp. There is a dodecahedral model, icosahedral model, and a third I don't know the name of, made of rhombic faces obtained by connecting vertices of the other two. The final image is all three models together. I'll use a ShopBot CNC router to cut out the pieces this week.
Vladimir Bulatov makes sculptures of fantastic variations on polyhedra and other geometric objects. His site is full of incredible metal, glass, and wooden geometric sculptures, including a full section on pendants and bracelets. Here are just a dozen or so of the hundreds of beautiful objects that he has produced.
Since today (11/11/11) is the last 6 digit binary date this century, I thought we should look at some kinetic binary calculators.
Here's my Sonobe Jasmine Dodecahedron built from Imatfaal's instructions.
It's Monday, time to highlight some of the community submissions posted to the Math Craft corkboard. One of these posts inspired me so much, I think it merits a closer look. Today, I present a "simple" method for making a golden spiral using just a straight edge, a compass, and a template, inspired by RJ Ellicock's golden ratio post.
Since it is now the holiday season, I thought we could spend this weekend making some baked goods that have mathematical patterns on them. In this post, we'll look at making cookies that have a fractal pattern based off of a modification of the pixel cookie technique.
Looking into mathematical quilting, I came across a community of mathematical knitters. Check out Dr. Sarah-Marie Belcastro's (research associate at Smith college and lecturer at U Mass Amherst) mathematical knitting resource page.
This is how my version of an origami Christmas tree turned out based on the instructions I posted awhile back. Cory also made a version from white glossy paper, which looks great. I opted for the green and brown look, but it wasn't easy.
Richard Sweeney is an incredible artist whose body of work consists mainly of sculptures made from paper. His art is often related to origami, and much of his work is related to geometrical forms. I personally really love his modular forms in paper. Many of them are based off of the platonic solids, which have been discussed in previous posts this week. Below are a small number of his sculptures, which are very geometric in nature.
Below, my construction of a Platonic Solid made from playing cards. To make your own, templates can be found at George Hart's site; there are also full step-by-step instructions here.
I finally got around to making the pentakis dodecahedron from the instructions in Math Craft admin Cory Poole's blog post. It's not tightened/straightened up yet because I just noticed that I have two black and white and two blue and green compound modules next to each other (but no purple and pink modules next to each other—to the math experts, this is a parity thing, as you can only have even numbers of modules paired up next to each other).
Cory's post with instructions and templates Here's my first attempt at the 30 squares model. I needed to be a little bit more careful in the measuring and cutting as not everything matches up - but it is still a really pleasing shape.
I wondered how silly you could get with sonobe, and had a bash at a buckyball, which is a fullerene (technically a truncated isocahedron; you can see a simple model here). It's twelve pentagons—each surrounded by 5 hexagons (20 in total)—making a football shape in England or a soccer ball shape in the USA.
Just watched PBS origami doc Between the Folds last night. If you haven't seen it, I highly recommend it. It's a beautiful film, really inspiring. Lots of Math Craft-related subject matter. Available instant on Netflix, or for rent on iTunes.
The initial idea for this project was to use magnets in the tips of the stellated octahedron and the intersections of the metal rings for either suspension or even a sort of weightless rotation. This turned out to be a bit too ambitious considering I'm working with found mirror and hot glue. So instead, I scrapped the magnets and went with simply mounting it on a skateboard bearing so it can freely rotate and not be bound to the base.
Did you know that you can "write" in polyhedra? I just stumbled across a $24.99 font called Divina Proportione. Created by Brazilian graphic designer Paulo W, the typeface is constructed with beautiful geometric renderings by the famous Renaissance printmaker Albrecht Dürer.
I made a Origami Valentine's day present for my Little Sister and Neice using heart and rose origami patterns I found on-line and put them in a backet with heart shaped lollipop I bought from Target.
One of my favorite simple projects is building two circle wobblers. I love how such a simple object amazes with its motion. The two circle wobbler is an object made out of two circles connected to each other in such a way that the center of mass of the object doesn't move up or down as it rolls. This means that it will roll very easily down a slight incline. It will also roll for a significant distance on a level surface if you start it by giving it a small push or even by blowing on it!
A source of inspiration... Models folded and photographed by Michal Kosmulski. There are only two sets of instructions on the site, but they are very well done. I wish he had covered more of the models. Here are a few I would like to tackle (I'll admit my eyes are bigger than my plate):
If you thought the last post on Two Circle Wobblers was wild, then wait until you see what happens when you build wobblers out of two half circles or two ellipses. In both of these cases, the center of gravity still remains constant in the vertical direction, allowing them to roll down the slightest of inclines or even travel a significant distance on a level surface if given a push or even when blown on.
Scrabble is definitely my pastime addiction of choice, but it's not the only game I frequent. I'm a big chess fan, crossword lover, and hooked on puzzles—any kind of puzzles. Logic puzzles, sudoko, and... the Rubik's Cube.
Mario Marín has made an incredible collection of models and sculptures based on polyhedra, often using everyday and readily available items. The site is in Spanish, but click on the links on the left and there are plenty of photographs, and more can be seen in Mario's blog.
Last Thursday's post demonstrated how to Make Yin-Yang Pillow boxes, which were based on equilateral triangles and squares. The units for making these boxes were created by Phillip Chapman-Bell, who runs an amazing origami blog and has a spectacular flickr photostream. Using these units, you can make also make 4 of the 5 platonic solids. I made an additional template based on the regular pentagon so that the dodecahedron can be built completing the set.
Eric Gjerde is a master of origami who devotes much of his energy on origami tessellations. Some of his pieces fold nearly flat, forming layers that add just a hint of depth. These pieces look beautiful when lit from behind, due to the variations in brightness and color. Other pieces utilize three dimensions more fully, with repeated structures rising out of the flat page.
It's Monday, which means once again, it's time to highlight some of the recent community submissions posted to the Math Craft corkboard. In this post, we'll also make a flexagon, which is a type of transformable object.
Oobject put together a neat compilation of the famous telephone inventor's love for tetrahedrons. Scroll down to see his collection of pyramids, building towers, buildings, boats, kites and planes—all made completely out of tiny tetrahedrons. Amazing.
I have a lot more images at hyperqbert's Profile • Instagram.
Erik Demaine is a Professor of Electronic Engineering and Comp Sci at MI, but he is also an origami folder who has had work displayed at the Museum of Modern Art in NYC. He makes some beautiful models and intricate puzzles, but in my opinion the really inspirational work is the curved creased models. In Erik's own words describing the above models: "Each piece in this series connects together multiple circular pieces of paper (between two and three full circles) to make a large circular ramp ...