From Chain-link Fence to Space-Spanning Mathematical Structures

(Proceedings pages 73–80)

Chain-link fence is constructed from intertwined zigzag wires. Such
a fence is basically a two-dimensional structure, which can be
extended infinitely in two directions. We describe various ways in
which zigzags can be intertwined to produce potentially infinite
three-dimensional structures. Next, we generalize the zigzags to
helices, and explore their possibilities to span space. These zigzags
and helices can be constructed from beams using miter joints.
Appropriate choices for the cross section and the kind of miter
joint results in artistically appealing sculptures. Several designs
were constructed in wood. Along the way, we discovered a nice
invariance theorem for helices.

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- zigzag-rhombic-octahedron-chain-3.mp4