Making Math Visible

Polylinks



These three beautiful constructions are challenging assembly puzzles.  Their apparent simplicity is deceiving and they will stretch the visualization and problem-solving skills of your students. 

Each structure derives from a familiar regular polyhedron---the tetrahedron, cube, and dodecahedron, respectively---yet the faces join together in a surprising way.  Instead of connecting edge-to-edge as polyhedral faces do, these polygons lock together by "linking elbows" in a symmetric entanglement.  Once they are built and handled for a while, their internal logic becomes clearer and they help students appreciate the richness of the structures to be found in the mathematical world.


 Four Triangles.  In this activity, students build a symmetric linkage of four equilateral triangles related to the tetrahedron, but surprisingly more difficult.

Six Squares.  Based on the familiar cube, but with a twist, students may be surprised at the level of difficulty involved when assembling six squares symmetrically.

Six Pentagons.  A much more challenging construction with an elegant regularity.  Students will make a beautiful object that manifests the joy of puzzle solving.

These three geometric structures are examples of "orderly tangles," first described in the 1970's by Alan Holden.  This video shows the construction of these three models.  For more polylinks and background on their history and applications, see this paper and this video.  An earlier version of these three activities using paper polygons instead of wood is described here:
G. Hart, "Regular Polylinks," Proceedings of Bridges Banff (2005), pp. 505-508.  (online copy)