By George Hart for the Museum of Mathematics

Paper is a versatile medium for experimentation and construction. Krystyna Burczyk has made beautiful sculptures by rolling paper squares to produce spiral corners that clasp together. They lock together without glue to create a kind of floral construction like modular origami but with spiral connections. This one has icosahedral symmetry—there are twelve purple locations with five-fold rotational symmetry. It isn’t traditional origami or kirigami, because of all the curves.

Below is a second example, this time with octahedral symmetry. There are six four-fold rotation points and eight three-fold rotation points.

An additional example below displays simple eight-fold rotational symmetry, making clear how the basic joint works.

There are many more examples in her galleries here and here. Krystina calls them simply “twirls,” but I like to call them “twirligami.”**More:**

- Math Monday: Found objects
- Math Monday: Kirigami polyhedra
- Math Monday: Mathematical lathe work
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- Math Monday: Mathematical beading
- Math Monday: Nailbanger’s Nightmare
- Math Monday: Recycling soda bottles into icosahedra
- Math Monday: Two-layer geodesic spheres
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- 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!
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- Introducing “Math Monday”

More information about this type of curler unit is available on the British Origami Society web site.

http://www.britishorigami.info/academic/curler.php