Our group of three (Pacus, Simran) attempted to create a Borromean Cube using three different colours of paperclips. The model cube consisted of 81 paperclips (81 / 3 = 27 of each of colour) where the green, red, and blue clips were oriented to be parallel to the x, y, and z-axes, respectfully (i.e. two clips are orthogonal if and only if they were a different colour).
It was fascinating looking up the history of the Borromean ring (the base unit of the cube) and how different cultures (independently) discovered the ring without having any knowledge of Knot Theory (branch of Topology) as it wasn't formalized until the late 18th century.
We had a significant amount of difficulty constructing the full cube due to our inability to bend/unbend the small paperclips and fit the ends into confined spaces (picture trying to fit a rope through a small loop without having any slack or being able to easily bend/unbend the rope). Instead we settled on a 'frame cube' which was comprised of (4/9)*81 = 36 paperclips (12 red, 12 green, and 12 blue). Our cube looked similar to the model cube except ours had the interior missing; it took on the appearance of a 3-dimensional cube drawn on a 2-dimensional piece of paper.
Our class presentation was an enjoyable experience - we outlined some Borromean Cube history, showed/discussed our creation, created our own link using our arms, (as there were three of us!) and even had the class attempt to create the base unit/link using the clips. Most of our colleagues were able to figure it out with little or no assistance from us. Overall, our group had fun with this math art project (personally, I haven't combined math with art in many years). If we were to build another cube (or similar) we'll have to remember to choose more pliable materials.
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