Is there a word for overlapping in a ring with no top or bottom element?
March 4, 2019 2:08 PM   Subscribe

The what's-wanted picture in this graphics question is an example. So are some traditional change purses, a table trick with knives, and some cockade ribbon rosettes. A formal description would be a series of n elements in which each element from 1 to n-1 overlaps the next element, and the nth element overlaps the 1st element.

Botanic rosettes aren't always examples, since they tend to be flattened spirals with a inner/upper member. Maybe some of them are circles of equal members, and there's a morphological term already?
posted by clew to Writing & Language (11 answers total) 4 users marked this as a favorite
Is this not a type of pinwheel?
posted by Hermione Granger at 2:52 PM on March 4, 2019

The butter knives are in a basket weave formation, which is also how you do a type of two-person carry.

I’ll be delighted if some term this specific and general exists, but basket weave covers one type, see also the basket weave box closing technique.
posted by SaltySalticid at 3:08 PM on March 4, 2019

If it ends up needing a temporary or permanent name, maybe "Möbius overlap"? Maybe /r/askscience, as I'm guessing this essentially is a question of topology?
posted by WCityMike at 3:09 PM on March 4, 2019

In heraldry, this arrangement is referred to as fretted, or interlaced. Generally it just means overlapping, but occasionally, a shape is specified. For an example, see the entry for the arms of Troutbeck under Salmon - three trout fretted in triangle.
posted by zamboni at 3:41 PM on March 4, 2019 [3 favorites]

Iris will carry a lot of the meaning, to some readers, but it’s not a formal term afaik.
posted by SaltySalticid at 3:51 PM on March 4, 2019 [2 favorites]

Perhaps a related kind of design may be the Borromean rings. In the wiki article, there is mention of "cyclic ordering" which I think could be applied to the rosette pattern you're looking for, though I don't think it appears to be standard terminology.
posted by mhum at 5:34 PM on March 4, 2019 [2 favorites]

The structural term for this is a reciprocal frame. It can be used to make some truly beautiful structures.
posted by q*ben at 7:55 PM on March 4, 2019 [7 favorites]

Seems almost related to Penrose stairs
posted by supercres at 8:11 PM on March 4, 2019

Related terms from Japanese mon heraldry:
Neji (twisted), where an overlapping charge is rotated around a center axis, e.g.
neji yotsu me
Kasane (stacked, heaped), overlapping, similar to the Western fretted, e.g.
migi mutsu oi kasane chōji
posted by zamboni at 5:20 AM on March 5, 2019

The wikipedia page for the painter's algorithm (used in 3D rendering) calls this "cyclic overlap," but searching for that term doesn't turn up anything outside of describing that one particular aspect of the algorithm.
posted by mustardayonnaise at 10:09 AM on March 5, 2019

Cyclic overlap is definitely what it is. All the neji kamon I can find use cyclic overlap. AFAICT all reciprocal trusses use cyclic overlap -- the bridge arch in the Wikipedia article is four connected four-element cycles, neat. And the Borromean knot certainly has it regarded ring by ring. I think that if you connected the / and \ elements of the Harrington's knot heraldic fret into two respective loops, you'd have a Borromean knot, so arguably the Harrington's knot has it (not in a way easy to generalize from).

What seems a little odd to me is that cyclic overlap appears as a common case in a lot of the other suggestions without being a category itself, e.g., fretty includes the c.o. fish and also cases equivalent to plain-weave. And yet, whenever I make something with cyclic overlap in the real world, handling the final-to-first overlap is a significant recognizable fussy part of the task.
posted by clew at 4:00 PM on March 11, 2019

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