Thing

Unit origami is a fun and creative pursuit. Oftentimes, units can be assembled in different ways. So you can create a different object based on how many units you have and how you assemble them. Consider the object below.


What is it exactly? I'm not sure. But it certainly is something.


This figure is made up of 24 identical units. Each unit was formed from one 3"x6" blue rectangle and one 3"x6" gold rectangle, folded together. The units were then assembled into the final form. It took me something like 3 hours and 45 minutes to create the rectangles (by ripping squares in half) and fold and assemble the units. I found this to be startlingly relaxing.

The pattern for the units may be found in Floral Origami Globes by Tomoko Fusè ("Alternate Fixes / Type II"... what does that mean?). I adapted the assembly instructions from a different part of the same book ("24-unit structure").

Cuboctahedron

This fancy fellow is a geometric figure known as a cuboctahedron. It is an example of a subset of origami known as unit origami, in which the folder creates many identical units (each from a single sheet of paper) and assembles them into a whole. Unit origami is ideally suited for realizing polyhedra (three-dimensional mathematical figures).

This cuboctahedron is constructed of 24 individual units (3 each of 8 different colors), each folded from a 6" square of origami paper. Folding patterns for each unit may be fond in the excellent book Unit Origami by Tomoko Fusè, under the name "Open Frame I — Bow-Tie Motif". Assembling units into various polyhedra is left as an exercise for the reader.

Thanks to the always-amazing Cafe Zing! for providing space for folding and photography.

The secret of the small dish

So what exactly is this "secret" we made reference to last week? Look and see, gentle viewer, and all will be revealed...


Here we see the "small dish" from last week, as well as a mirror-image version. (Why a mirror-image version? That's part of the secret, folks.)


Here we see the same two dishes, each with three "flaps" extended. The flaps are normally inserted into the base of the bowl as part of the locking mechanism. However, they can be extended...


...and combined! We are now privy to the secret: the small dish can be combined with it's mirror-image counterpart to create this geometric figure, known as a regular icosahedron. (A regular icosahedron is a solid figure that consists of 20 identical triangles. Geeks like me will also recognize it as a d20.) Such shapes have been studied by mathematicians for thousands of years, and are favorite subjects for unit origami designers.

The icosahedron was constructed from 12 sheets of 5-7/8" square origami paper and stands roughly 5" tall. It was designed by Tomoko Fuse; a folding pattern for it may be found in her book Unit Origami. (Just like last week, huh?)

Rice bowls

Here we have a pair of rice bowls. These bowls are examples of "modular" or "unit origami", a style of origami in which many identical units are created and locked together via folding alone to create the final model. Two different (but similar) kinds of units were used in the creation of these bowls; each bowl consists of 3 of the first kind and 3 of the second kind.

Astute viewers may notice that the bowls are similar in pattern. They are actually from the same pattern; slight changes in the shaping folds of the units account for the difference in shape. The bowl on the left is clearly triangular. The bowl on the right is referred to by its designer as a "small dish" and has special properties. What are these properties? They will be revealed in next week's post.

Notice the interior spiral pattern of the bowls.


Each rice bowl was created from 6 sheets of 5-7/8" square origami paper. Each is approximately 2-1/2" deep and 5" to 5-1/4" wide. The bowls were designed by Tomoko Fuse. The folding pattern for both may be found in her book Unit Origami.

Leafy box

My friend Liz is moving away. *sniff, sob* So I made her a box.


The leafy box is almost exactly the same design as the purple swirly box, but made with different paper. It's very thin and delicate -- almost translucent -- with small leaves embedded throughout. I picked this paper up (as a huge sheet) and sliced it down to a manageable size.

The box is made from 8 units, each made from a 6" square of paper. I didn't have a chance to measure it before I gave it away, but ideally the lid should be 3-3/16" square. (In reality it's probably closer to 3-3/8".) The design is by Tomoko Fuse, and may be found in her book Origami Boxes.

Silver and gold cube

This is the silver and gold cube (aka the "Burl Ives cube") which currently resides at my friend Kate's house. This lovely modular design consists of 12 identical units fitted together into a cube and takes advantage of the dual-sidedness of origami paper, incorporating the reverse side into the pattern.

My first attempt at this design was affectionately called the "skunk box"; it was black with white stripes. Alas, it did not survive moving day, perishing along with some of my other, fragile, possessions.

The silver and gold box is notable because I did not use two-sided silver-and-gold foil paper. (I now own such paper, but that is beside the point.) I was pretty set on the color scheme, so I actually made 12 separate units consisting of 1 sheet of gold foil placed atop 1 sheet of silver foil very carefully folded together as if it was one piece. (A saner person would have glued the sheets together.) So this piece is ultimately constructed of a hefty 24 sheets of paper.

This cube was designed by Lewis Simon. A folding sequence for it may be found in Practical Origami by Rick Beech.

Purple swirly box

I made this box for my friend Jenny (as opposed to Jen, Jen, Jen, Jennifer, and Jen). I ended up folding this box outside Cafe Zing. It was the first nice weather of the year, and I sat beneath a blossoming cherry tree. Every time the wind blew, I was showered with a cascade of petals.

This is one of a series of boxes by Tomoko Fuse that are very fun to fold. The base consists of four units that sort of resemble wings folded flat (not really, but that's the only way I can think to describe them) linked together in a hollow ring. Once assembled into the ring, the "wings" are lowered and flattened into a surprisingly solid base.


This box was folded from 8 sheets of standard 5 7/8" origami paper. The finished box is 3 3/8" square and 1 3/4" deep. Folding instructions may be found in Fuse's Origami Boxes.

Hot and cool cubes

The hot and cool cubes were fun models to make. When I make a box, I usually pick out the colors I want to use first and then decide on the design. With other types of unit origami, however, I generally choose my design first and then decide on the colors. In this case, I decided I wanted to make two interlocking cubes and then decided to do them in hot and warm colors. It was an easy decision. I like using the six primary and secondary colors all together (as seen in earlier posts), and the three-dimensional symmetry of the cube model lends itself well to using three colors apiece. I think the decision to divide the colors into hot and cold (instead of some other, arbitrary divisions) was an unconscious desire to maximize contrast between the two cubes.

The units (and interlocking cubes themselves) were designed by Tomoko Fuse. Folding patterns for them may be found in her excellent book Unit Origami.

Truncated tetrahedron

I am passionate about mathematics. I believe this is one of the reasons I was so irresistably drawn to origami; it is a very mathematical art. There is beauty not only in the final form, but in the analysis of the shape, the creases, the angles... discovering the relationship between simple lines and the final opus.

Others have also notices the relationship between mathematics and origami and used it to create interesting works. In particular, the creation of mathematical structures known as polyhedra can be created in a very natural way by use of unit origami.

This model (or technically, the skeleton of this model) is a semiregular polyhedron known as a truncated tetrahedron -- that is, a solid figure made up of 4 hexagons and 4 triangles. It was designed by Tomoko Fuse and consists of 18 separate, identical units folded from 3" x 6" rectangles. The paper is some sort of Italian print that I purchased and cut into the appropriate size. I was not able to measure it, but my detailed analysis of the fold pattern and structure indicates that it should be about 4 7/8" tall. Did I mention that I am passionate about mathematics?

This model is shown in its native habitat: on top of one of Zing!'s coffee makers. Folding instructions may be found in Fuse's book Unit Polyhedron Origami.

Color wheel box

When planning this box for my friend Jen (one of my friends Jen, actually), I asked her for her favorite color. After quite a bit of thought, she responded, "All of them." Thus, the color wheel box was born!

This box is one of the more complex box designs of Tomoko Fuse. The majority of her boxes consist of 8 units, and she has created hexagonal boxes out of as few as 4 units -- this box consists of 12 units. The biggest advantage of having so many units is the ability to use many colors, creating a nice rainbow effect. In addition, it's one of the more solid and heavy boxes I've made.

The exteriors and interiors of both lid and base can be seen in the photos below. I especially love the patterns created in the interiors of both components.

This box was constructed from 12 sheets of standard 5" origami paper of 6 distinct colors. The assembled box is 3 1/4" wide side-to-side (3 1/2" corner-to-corner) and 1 5/8" deep. the design is available in Fuse's book Origami Boxes.

Octagonal box

This box is a going-away present I made for my friend Rachel, who is moving to California in a couple of weeks. She is actually the person who gave me the idea to post pictures of my origami on the Web, so it's only right that her present be the first picture.

This is a composite or "unit origami" model. The lid and base are each made from four sheets of standard origami paper cut to 4" squares. When assembled, the lid is a bit over 3 1/4" from side to side, and the base is a bit smaller. The white portions of the box are the undersides of the paper.

This design is by my favorite designer, Tomoko Fuse, from her book Fabulous Origami Boxes (truth in advertising). The lid (but not the base) also appear in her book Origami Boxes.

In the pictures below you can see the assembled box, the exteriors of both lid and base, and the interiors of both lid and base.