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: