Ornament: Water Bomb base modular

The technique of making sets of individual models, called units or modulars, and putting them together to form the final model is one of the modern innovations in origami. The models tend to be of geometric forms as opposed to animals or plants. The cube that can be turned into a rose is an exception and is indeed an exceptional model with fascinating locks and symmetries. The study of modular origami contains substantial mathematics. The books of Rona Gurkewitz and Bennett Arnstein are especially good for the exposition on systems of folding.

 Here is an example of a simple model that can serve as an introduction to modular origami. The images are pictures taken with a digital camera.

 1. The unit is the water bomb base: the tent that collapses to be a triangle, with two flaps on each side. Make 6 of these in sets of 2 for each of three colors. We will assume the colors are red, white, and blue.

 2. Each set of two matching units will be oriented to face each other, bottom facing bottom.

There are three sets corresponding to the three dimensions of space. You can think of it as up-and-down, left-and-right, and forward-and-backward. Using more mathematical language, define a typical coordinate system with x, y, and z-axes. The x-y plane is parallel to the floor and the z-axis corresponds to up and down. Pick up one red unit and hold it so that it points to the left, and the four flaps (triangles) form a cross: two lie in a plane parallel to the floor, and one is straight up and the other straight down. The point is towards your palm, and the open edges are just beyond your fingertips.

3. A feature of all modular models is the way parts of the units fit into parts of other units. These are sometimes called 'pockets and tabs'. The horizontal flaps of this first modular will form pockets, and the vertical flaps will form tabs. Pick up a white unit. Holding it with the bottom of the four flaps facing you, slide the left horizontal white flap into the far horizontal red flap.

4. The bottoms of the red and white modulars are both in vertical planes. The blue modular must now go on top with its bottom in a horizontal plane.

The red is covering a white flap. Therefore, the blue modular must be placed so that it covers a red flap and is covered by a white flap.

5. The challenge now is to complete the model! Take the second red unit. You want it to be opposite the first red unit and have the flaps in the horizontal plane on the outside. Orient it to be facing the first red unit, and poke a flap into the blue flap opposite the one that is over the flap of the first red unit. Similarly, poke the mate of the white flap that pokes into the other red unit into this red unit.

6. Continue with the other white and the other blue.

How does this work? It may be advantageous to construct a table of the pockets and pokes, with a row corresponding to a unit. In the table, the units are given names. For example, the two red units are called red1 and red2. The table indicates the positioning of each of the four flaps of each unit.
Name of unit flap 1 flap 2 flap 3 flap 4
red1 under blue1 over white1 under blue2 over white2
red2 under blue1 over white1 under blue2 over white2
white1 over blue1 under red1 over blue2 under red2
white2 over blue1 under red1 over blue2 under red2
blue1 over red1  under white1 over red2 under white2
blue2 over red1 under white1 over red2 under white2


Every unit has 4 flaps. There are 5 other units. Every unit is connected in some way to 4 of the 5 other units. The one it is not connected to is the unit of the same color. Two of the flaps are pokes, and two are pockets. This level of analysis does not have to be made explicit immediately but it can be helpful.

 Ask the students to take their models apart. Note that this is not difficult to do because the connections do not have the type of locking mechanisms that many other more complex and necessarily more robust modulars have. Ask them to visualize how it goes together and then put the model together, visualizing the next step before they do it.

 Do organize the students to teach this model to each other with rehearsals and collaboration on the teaching methods. It is sufficiently challenging that students will appreciate any especially evocative methods of communication.

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