By George Hart for the Museum of Mathematics

Each year I visit the annual Origami convention in New York City, and this year, as always, I was impressed by the wide range of works on display. The mathematical examples get more sophisticated each year. Here are just four examples to illustrate a range of folding styles.

The above is the symmetric compound of six pentagonal prisms, designed and folded by Daniel Kwan.

This hexagonal swirl tessellation was designed and then folded from one sheet of paper by Jon Tucker.

This pentagonal torus is a modular design assembled from a great many small folded units. It is designed by Heinz Strobl and folded by Faye Goldman.

And Brian Chan designed and folded this amazingly complex fractal from a single sheet of paper. It is a model of a Romanesco broccoli, true even to the Fibonacci numbers displayed in its phyllotaxis. There are eight spirals in one direction and thirteen in the other direction. Many books and internet resources are available if you want to start making your own mathematical origami.

**More:**

- Math Monday: The twisted torus
- Math Monday: Binder clip constructions
- Math Monday: Twirligami
- Math Monday: Found objects
- Math Monday: Kirigami polyhedra
- Math Monday: Mathematical lathe work
- Math Monday: Modular Kirigami
- Math Monday: Mathematical beading
- Math Monday: Nailbanger’s Nightmare
- Math Monday: Recycling soda bottles into icosahedra
- Math Monday: Two-layer geodesic spheres
- Math Monday: What to make with golf balls?
- Math Monday: Knitted cellular automaton tea cosy
- Math Monday: Whittling links and knots
- Math Monday: Magnet constructions
- Math Monday: Hexagonal stick arrangements
- Math Monday: Paper plate geometry
- Math Monday: 3D Hilbert curve from plumbing supplies
- Math Monday: Math-play with your food
- Math Monday: Mathematical art in the lava
- Math Monday: Balloon polyhedra
- Math Monday: Sierpinski tetrahedron
- Math Monday: Skewer hyperboloid
- Math Monday: Morton Bradley sculpture
- Math Monday: Tetraxis puzzle
- Math Monday: Giant burr puzzles
- Math Monday: Fractal polyhedra clusters
- Math Monday: Giant SOMA puzzle
- Math Monday: Tie your bagel in a knot!
- Math Monday: Playing card constructions
- Introducing “Math Monday”

Even more phenomenal things are in the exquisite, Peabody Award winning documentary, Between the Folds. Trailer, DVD, etc. at http://BetweenTheFolds.com !