By George Hart for the Museum of Mathematics


Kirigami is a traditional art of cutting paper. Ulrich Mikloweit takes it a step further by assembling many pieces of kirigami into intricate mathematical models. This is a snub dodecadodecahedron made from 924 cut and colored facets.

ulrich1 Math Monday: Kirigami polyhedra

Ulrich has dedicated years to making hundreds of such hand-cut models, which can be seen on his website.

uhlrich display case Math Monday: Kirigami polyhedra

The simplest possible polyhedron is the tetrahedron. It consists of just four triangles, but it is still visually interesting when made by Ulrich with his hand-cutting techniques.


This compound of five tetrahedra (one in each of five colors) shows how the faces continue in the interior of the form and how the cutouts allow you to see the many levels of internal structure.



Gareth Branwyn

Gareth Branwyn is a freelancer writer and the former Editorial Director of Maker Media. He is the author or editor of a dozen books on technology, DIY, and geek culture, including the first book about the web (Mosaic Quick Tour) and the Absolute Beginner’s Guide to Building Robots. He is currently working on a best-of collection of his writing, called Borg Like Me.

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