Mathematical Impressions: Regular Polylinks

A video illustrating the beautiful geometry behind symmetrical linkages of regular polygons.

First described by the chemist Alan Holden in the 1970s and 1980s, regular polylinks are symmetrical linkages of regular polygons. They are beautiful mathematical objects, without significant applications as yet. This video shows a variety of examples using wood, metal, plastic, paper and computer animations. As regular polylinks become more widely known, perhaps someone will find interesting applications for them. The wood puzzles consisting of 12 pentagons and 10 triangles were designed and built by Teacher Lin and Sculptor Wu of the Kaohsiung Puzzle Club in Taiwan.

Further Reading

Holden, Alan. Shapes, Space, and Symmetry. Columbia University Press, 1971.

Holden, Alan. Orderly Tangles: Cloverleafs, Gordian Knots, and Regular Polylinks. Columbia University Press, 1983.

Hart, George. “Orderly Tangles Revisited.” In Mathematical Wizardry for a Gardner, edited by Ed Pegg Jr., Alan H. Schoen, and Tom Rodgers, 187-210. A. K. Peters, 2009.

Jespersen, Bjarne. Woodcarving Magic: How to Transform a Single Block of Wood Into Impossible Shapes. Fox Chapel Publishing, 2012.

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