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
In this activity, students build a symmetric linkage of four
equilateral triangles related to the tetrahedron, but
surprisingly more difficult.
Based on the familiar cube, but with a twist, students may
be surprised at the level of difficulty involved when
assembling six squares symmetrically.
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:
(2005), pp. 505-508. (online