These 3D shapes have a lot of symmetry, though not as much as the Platonic solids. To enable locomotion in multiple shape configurations, a novel body architecture comprising modular, actuated leg mechanisms, is designed. Questions about larger models will lead you to the Archimedean solids and the Johnson solids. The robot, currently, with tethered electrical connections for power and control is manufactured using laminate fabrication and assembled using origami pop-up techniques. Questions about coloring will lead you to the mathematics of graphs and networks (and big questions that remained unsolved for many centuries). One seemingly innocent question can easily lead to a mathematical rabbit hole. Each folded from 6 squares of origami paper. Diagrams in Geometric Origami: The Art of Modular Paper Sculpture by Michael G. Diagrams in Fun Origami World by Makoto Yamaguchi. They were originally used for incense and potpourri which I guess is where the name comes from. The word kusudama literally means Medicine Ball when translated from Japanese. Kusudamas are modular origami models where multiple units are fit together to form a ball-like shape. Simply click on a model to view the diagrams. Diagrams in Fun Origami World by Makoto Yamaguchi. 30 Absolutely Beautiful Origami Kusudamas. Even if you're a complete paper folding beginner you should be able to fold most of what's here. 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?) Below you'll find instructions for 120+ easy to fold origami models. Sonobe units, like these ones piled in a stack, can be put together to create 3D shapes. So, for a little effort you are rewarded with a vast number of models to explore. 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. That's where you use several pieces of folded paper as "building blocks" to create a larger, often symmetrical structure. Any piece of origami will contain mathematical ideas and skills, and can take you on a fascinating, creative journey.Īs a geometer (mathematician who studies geometry), my favorite technique is modular origami. I'm a mathematician whose hobby is origami, and I love introducing people to mathematical ideas through crafts like paper folding. Both activities, however, share similar skills: precision, the ability to follow an algorithm, an intuition for shape, and a search for pattern and symmetry.
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