Plaited Polyhedra: “Stimulating and Practical”

“Not only are these shapes attractive to the eye, they provide yet another example of the way apparently dull and complex research often comes up with something stimulating and practical.”

This 1960 newsreel, about an unconventional teaching method for mathematics used by Southampton schoolmaster, Robert Pargeter, focuses on his plaiting technique for weaving polyhedral models. (via: British Pathé)

The film makes much of the fact that the models do not require gluing. Not needing glue is also seen as a good thing in package design, when it can be achieved. Buthere the narrator lightly suggests that glue “somehow doesn’t seem to mix with school boys” which made me wonder why. (Because it’s messy? Because 1960s school boys sniff glue?)

The “19th Century doctor” mentioned as the inspiration for Pargeter’s project must have been John Gorham and his 1888 “A System for the Construction of Crystal Models on the Type of an Ordinary Plait” must be the “article” that the film briefly alludes to.

What is not mentioned is that, in 1959, Pargeter, himself, published an article in The Mathematical Gazette, entitled “Plaited Polyhedra.” A page from that article appears below…

As much as I love it when package design goes polyhedral (see examples of rhombic dodecahedron and stella octangula) packaging constructed in the manner of Pargeter’s plaiting of a great dodecahedron, is perhaps, not so practical.

Although plaited baskets are doubtless one of the earliest precursors to modern packaging. And, in fact, John Edminster’s tri-tuck closure and other overlapping flaps show that certain degree of “plaiting” is already in evidence in the construction of folding cartons.

Still, complex containers requiring this type of skill are surely more of a craft than an industry. It’s hard to imagine what sort of polyhedral loom would be needed to automate a “Pargeter’s plaited packaging” method.

And yet again, if the Jacquard loom could automate the weaving of impossibly complex fabrics in the 1800s —laying the groundwork for what would eventually become computer programing— it might be a mistake to assume that complexity makes a concept impractical.

If you’re wondering who that guy is at the very beginning, I figure they must have segued from a previous segment in a series of newsreels. That guy must beRobert Welch who designed modern. stainless steel cutlery.

(One more stimulating 1880 mathematical model from Gorham, after the fold…)

See also: Polyhedral Models and Interesting and Practical

–Randy Ludacer

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