![]() These 3D shapes have a lot of symmetry, though not as much as the Platonic solids. Questions about larger models will lead you to the Archimedean solids and the Johnson solids. Fold the bottom right corner up diagonally. Next, fold the top and bottom edges to the central crease. Fold the bottom edge of the paper up to the top and unfold, creating a horizontal crease. Start with a piece of square paper, white side up if it has one. Questions about coloring will lead you to the mathematics of graphs and networks (and big questions that remained unsolved for many centuries). For this tutorial, well be making a triangular shape using nine Sonobe units. One seemingly innocent question can easily lead to a mathematical rabbit hole. ![]() Once you've mastered the basic structure of each 3D shape, you may find yourself (as others have done) pondering deeper mathematical questions.Ĭan you arrange the sonobe units so two units of the same color never touch, if you only have three colors?Īre larger symmetric shapes possible? (Answer: yes!)Īre there relationships between the different 3D shapes? (For example, the icosahedron is basically built of triangles, but can you spot the pentagons lurking within? Or the triangles in the dodecahedron?) Sonobe units, like these ones piled in a stack, can be put together to create 3D shapes. Since then, I’ve taught hundreds of students to fold them. The first piece of modular origami that I learned to fold was a Sonobe Cube. I’ve been playing around with modular origami (also called unit origami) since my first year of teaching. LaFosse) is a variation on the Sonobe Cube. ![]() So, for a little effort you are rewarded with a vast number of models to explore. The Harlequin Cube (designed by Michael G. Many modular origami patterns, although they may use different units, have a similar method of combining units into a bigger creation. The building blocks, called units, are typically straightforward to fold the mathematical skill comes in assembling the larger structure and discovering the patterns within them. (Interestingly, it’s not possible to build a tetrahedron and dodecahedron from sonobe units). That's where you use several pieces of folded paper as "building blocks" to create a larger, often symmetrical structure. You will need six sonobe units to make a cube like the yellow-blue-green one pictured above, 12 to make an octahedron (the red-pink-purple one), and 30 to make an icosahedron (the golden one). The 'building blocks' of origami modelsĪs a geometer (mathematician who studies geometry), my favorite technique is modular origami. Any piece of origami will contain mathematical ideas and skills, and can take you on a fascinating, creative journey. I'm a mathematician whose hobby is origami, and I love introducing people to mathematical ideas through crafts like paper folding. If you could do this then you probably could make the object. Thats why Imatfaal was trying to figure out if you could make the sonobe units form an equiateral triangle. The first, which is called ‘Toshie’s jewel’ or ‘Crane egg’, is made up of three (3) units.Both activities, however, share similar skills: precision, the ability to follow an algorithm, an intuition for shape, and a search for pattern and symmetry. The only ones using the sonobe unit that I have seen are the cube and the dodecahedron. ![]() The models I assembled corresponding with these units are shown below, the last of which is the same model shown at the top of this page. Here are three pinwheel-turned-Sonobe units: On the other hand, the traditional pinwheel model as shown below may be viewed as a double parallelogram: one horizontal and one vertical.īy making the upper and lower flaps of the pinwheel ‘disappear’, we are able to transform it into a Sonobe unit. The Sonobe unit has the shape of a parallelogram which is typically folded from a square paper starting with the cupboard base. Attributed to Mitsunobu Sonobe in the 70s, the Sonobe unit is a very popular building block in modular origami and a lot of polyhedron models based on it, as well as instructions and diagrams on how to fold the unit, is found in the Internet. I made this cube model using six (6) units of the traditional Japanese pinwheel which I folded into Sonobe units.
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