By George Hart for the Museum of Mathematics


With paper and scissors and patience, you can make an amazing variety of mathematical forms. The paper sculpture below consists of twenty identical components that form a complex linkage. They lock together without glue in a very symmetric arrangement.


If you want to try this, the template for the construction is the blue shape below. Twenty copies are required. Note that there will be twelve 5-sided openings like the one at the center of the above image.


With sixty copies of the above “3”-shaped template, one can make thirty copies of the “8” shape, which interlock to form the construction below. It also holds together without glue.


“Kirigami” is the Japanese art of paper cutting. Because these constructions involve many identical copies of a single module, I call them “Modular Kirigami.” For more examples and larger-scale templates, see this paper [PDF].