Zip ties are a great way to tie things together, from cables to people. They are extremely difficult to take apart non-destructively once they have been “zipped”, so you have to be careful when trying to build something out of them, but having a built in connection mechanism makes building things “easy”.
Which is to say that it’s easy to build things as long as you want to make long strips or rings of zip tie, but there is no real way to “branch” your rings. Pentagon? easy. Tetrahedron? hrm…
Fortunately, we don’t need nodes of degree greater than 2 to make cool structures. By interleaving rings of zip ties, we can make compounds of regular polygons. These structures are referred to as regular polylinks or orderly tangles.
Orderly tangles are a nice way to illustrate symmetric colorings. I made this orderly tangle of four zip tie triangles out of four different colors of zip tie. The resulting structure has octahedral symmetry. If you think of the zip ties as representing edges, and the spaces between them as faces, the resulting structure in the middle can be thought of as a woven cuboctahedron.
Since the zip tie triangles have a chirality to them, the final sculpture also has some chirality. Keeping the chirality straight during construction may be the most difficult part of making this piece.
Many other tangles are possible. A tangle of six pentagons is tricky (and I don’t have that many colors of zip tie), but would demonstrate a similar symmetric coloring of the icosahedral group. Let me know if you try making one!