Friday, December 30, 2016

Simple solids

After folding a new-and-improved k-dron a year and a half ago, I was thinking a lot about folding closed 3D solids with flat faces in a similar manner. As a busy graduate student, I've kept myself busy over the past couple of months. The idea came up again recently and I decided to try something simple as a test. What simpler shape than a tetrahedron?

My idea was to try to use paper efficiently and equally for all faces and edges. Instead of having every face join at the edge, I opted to have all but one edge not touching. After some trial and error I found a simple lock from where two of the edges come together, as well as the reference for a 15 degree angle (which I have no doubt has been found before).

I'm happy with the result, despite the fact that the lock ruins the otherwise clean faces of the model. There is way to get the excess paper from the sides of the locking face to hold a lock behind it, but it doesn't hold as tightly. Let's just say the colour change on the lock means the tetrahedron could double as a snow-capped mountain or Christmas tree.

Tetrahedron and intersecting tetrahedra


Friday, February 19, 2016

Eight months to publication

When I was at the Origami USA annual convention last year, I had a lot more time than usual to design. Anyone who went to the exhibition might have seen my haphazard display that included "Walrus (designed last night)". I also spent some time doodling with other designers, and at one point a came up with something that looked fishy — in the literal sense. Unless you count the dolphin, I haven't really designed a fish that I've been satisfied with. The idea was very simple (based on a preliminary base), but with the original colour changes and the big sail on the back the original design didn't look like anything in particular. I wanted to make it into a marlin or a sailfish at the time, but I couldn't decide how to fix the colours. Here is the CP for what I'd come up with:

In the past couple months, I found out that my school has a new origami club so I decided to go and teach/play around with designs. I kept coming back to this designs, making an iteration about once a week. I was finally satisfied with the design just the other day, so I folded the final version to post online, looked at pictures of marlins and sailfish to decide which it was and realized it looked like neither. Luckily, realized that to make it look more like a marlin I just needed to add a ventral fin and change the tail colour and I had enough extra paper for both with the same base.


I would like to say that I'll get out the other ideas from OUSA soon, but clearly it might take a bit more time. In the time since my last post I transferred to a Ph.D. and became a student athlete so my schedule has been pretty full! Fortunately, having a local origami club gives me the excuse to make some time to design new things.

Saturday, September 5, 2015


Sometime around last December I decided that I wanted to fold a walrus. I've seen a several orgami walruses, but most that I remembered were either very anatomically correct or focused on only the face. My goal with the walrus was to make a cartoonish model that focused more on the volume. In other words, I wanted to make a ball of blubber with eyes, tusks and flippers.

I didn't have much time to design until near the Origami USA convention in New York, and during the convention I came up with something that I am happy with. Here is the crease pattern, which I should not will not lie flat:

Adding details after folding the base is fairly straightforward. All that remains is a couple thinning folds to the front flippers and tusks as well as some folds to bring out the eye flaps. The most important part is making the model round. This model was originally intended to be wetfolded, but unfortunately I didn't have any good paper for wetfolding when I made the final model.

Walrus, Ryan MacDonell

Walrus, Ryan MacDonell

This is one of a few models that I had time to design, so with any luck I should have time to fix up and post the others in the next month or so.

Monday, April 13, 2015

Finally finished again

I haven't been able to design anything in a long time, in part due to "folder's block" as well as having recently spent a summer traveling before starting graduate school. As it turns out, although there is less stress involved relative to my undergraduate years, I don't have as much free time as I'd hoped.

Seven years ago, I attempted to fold a geometric shaped known as a k-dron. Although I didn't mention it in that blog post, much of the "design" work was just free folding to get a final shape that looked right. It's safe to say that I wasn't really satisfied with the end product but I posted it online anyway (as I often did then).

Last week, I found out about the Weaire-Phelan structure which is (at the moment) the most efficient known unit for closed packing of 3D space (in terms of surface area to volume). I soon started trying to figure out it's structure and symmetry. After a while I thought about how it might be folded, considering it has both concave and convex parts. This lead me back to the k-dron, which has a single convex point.

My k-dron work this time consisted of me working with accurate angles and proportions on Inkscape. After a couple trials, I figured noticed the following: To use paper efficiently, if two sides of a face don't match up I at least need to have the vertices matching, which may mean "cutting" a face and pleating it together. This is a bit clearer from the following image.

The above image shows how I decided to split the central face of the model in order to match the vertices with the sides. I also split the five-sided face so that I could match edges. I first drew the layout for a 14x14 grid, then added a unit all around to be folded inside and lock the model. Keeping the bottom triangles at a 90 degree angle with the sides, I noticed several different references for the model, shown as black lines. Most are just extensions of folds matching with a grid line. The most important are the references circled in red. Two points on the grid lead to a very good approximation of the angle. From those lines all the rest of the difficult angles can be folded. Based on those references, I drew this CP:

The model didn't really satisfy me without a bottom face, so I decided to make a base to fit it.

The two parts fit together similar to a masu box. I know that I could achieve a similar result by using a longer rectangle but the base gives some added support to the model. The result is quite nice, with only two seams showing on the full surface area. The real magic comes from making two units, which fit together to make a cube without gaps.

K-dron, Ryan MacDonell

K-dron, Ryan MacDonell

I realized afterwards that, like the Weaire-Phelan structure that started my thoughts about geometry, the k-dron will also span 3D space because two of them make a cube. I'm glad that inspiration managed it break it's way through the "folder's block," and with any luck it might persist. I've had a lot of ideas in the past year so it's only a matter of deciding how to fold them. I plan to attend the OUSA convention again this year which may really help get those ideas out.

Monday, January 13, 2014

12 Days of Christmas: Hours of Folding

This took me a little while to post due to a lot of sudden events (e.g. diverted flights, cancelled courses and sudden chess tournaments) over the past week. I've seen at least one project in the past where a folder (namely Andrew Hudson with "Octagons for October") designed a new model every day for a certain amount of time (I believe Andrew did a full month). I decided to take up a similar project myself, except with only 12 holiday themed models for the 12 days of Christmas. I decided soon after I started that it would be best if I posted all of the designs on a single blog post instead of writing a short post every day.

On the first day of Christmas (i.e. Christmas Day) I already had a minimal colour change model in mind. The model is named "Stocking on Red", and as the name suggests it is meant to show only the white heel, tow and cuff of a Christmas stocking. The model is made from an offset windmill base (both in angle and centre).

Stocking on Red, Ryan MacDonell

The next model was some berries leaves of holly. To be honest, I don't think I've ever encountered real holly, just plastic Christmas decorations. The model is from a waterbomb base, with 3 corners for leaves and a corner for the berries.

Holly, Ryan MacDonell

Day 3 brought an idea that's been done before by other folders, but I decided to try something of my own. The idea is to fold a wrapped gift box with a bow. For paper efficiency, I only made a 3-sided box; however, as long as the shadow doesn't give it away it seems like a full box. The size and shape can be varied too, as shown in the photo.

Wrapped Gift, Ryan MacDonell

The fourth day was another simple colour change model. I figured out the night before that I could fold a simple manger from a pig base, so I just folded is some more paper to make a colour changed baby.

Baby in Manger, Ryan MacDonell

The fifth model is probably my favourite, and it seemed to be pretty popular as well. Despite the fact that we celebrate Canadians have Thanksgiving, turkey is still a very popular food at Christmas. I remembered seeing Joseph Wu's roast chicken, so with that in mind I folded a roast turkey from a waterbomb base. The model is completely closed, and the folding sequence is simple enough that I'll probably make some diagrams.

Turkey, Ryan MacDonell

After the turkey, I was running a bit short on ideas that were quick to design and fold. I remembered seeing a few traditional models made 3D (such as in one of the Tanteidan magazines), so with that in mind I designed a sleigh. The result is probably my least favourite design from the series, but I feel like the idea could be used to make something much better looking.

Sleigh, Ryan MacDonell

Day 7 was new years eve, so I thought it would be appropriate to fold something that represented 2013. A few things came to mind, but I ended up folding Canada's international news maker of the year: Toronto's crack cocaine smoking mayor, Rob Ford. The model is based around using the diagonal for the colour change tie.

Mayor Ford, Ryan MacDonell

The eighth day of Christmas was New Years day, so naturally I folded my interpretation of fireworks. The model is based on the simple idea of using raw edges for colour change. It should be possible to fold the model from the photo. Note that the centre of the burst is at the centre of the paper.

Fireworks, Ryan MacDonell

My ninth model was another rushed idea to get it done in a day. I've been thinking of ideas for a Santa model for over a year now. My idea was to have the beard come from the centre of the paper, and I ended up with a star shape. As a result, I called it "Santa Star". Without the hat, the shape also reminds me of the abominable snowman from Monsters Inc.

Santa Star, Ryan MacDonell

The model for the tenth day has to be one of my favourites, right after the turkey. In 2010, Vancouver hosted the winter Olympics and HBC sold red mittens with a white maple leaf on the palm. The mittens were extremely popular, and for a while even on the opposite side of the country you couldn't go anywhere without seeing them. The model is from half of a windmill base.

Olympic Mitten, Ryan MacDonell

On day 11 I folded a model that I'd been thinking of since the beginning of the series: a camel. In particular, it is a dromedary camel (one hump). I wasn't aware before looking at reference images how oddly shaped camels are. I'm happy with the result, but I realized that a 15 cm square is a bit too small for this model.

Dromedary Camel, Ryan MacDonell

The final model was done quickly, but it ended up being another of my favourite models from this project. I wanted to fold another Christmas tree, this time with colour change from the centre. The model is based off of a windmill base (like most colour change models of this type) with some extra paper from around the edge. The CP is particularly interesting, so I hope to see some other people try it out!

Christmas Tree 2, Ryan MacDonell

All in all, I'm very happy with how the project turned out. Even with the rushed models, having a deadline for designing helped me to come up with new ideas and think of interesting subjects each day. I might not do another project like this for a while, but this has certainly inspired me to spend a bit more time playing with design ideas.