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By George Hart for the Museum of Mathematics

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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.

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

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

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

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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