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Friday, December 11, 2015

Pentagonal Tessellations - The Mathematics That Goes Into Making Something Repeat

Tessellations are very challenging from a design perspective. When designing fabrics you have a whole host of ways in which you might approach a fabric. The basics are changing the weaving techniques and keeping a solid colour and/or adding a hidden colour (through the warp). In this case you might choose a basket weave, a satin, a grosgrain, a grenadine, a hop sack, an ottoman or a garza for example. That gets you texture in a solid colour which is as much as some men want to go for. You can make an entire living out of this if you get it right. I can't tell you how many exactly but I would assume that hundreds of Charvet grenadine ties in solid colours would sell each Parisian summer as men flock to make a pilgrimage to the Place Vendome store.

Then there is the art of the motif or recurring image, be it a star, a horse, a gun or a bikini clad lady as one designer in the States specialises in. You can then add into genre of silks things like paisleys and geometric repeats which sit on top of the base warp whilst weaving the weft, usually on a satin, well at least that is what I am most familiar with.

Finally there is each season a wave of tessellations which have a very interesting effect on a silk and can really alter the appearance of the fabric both in how it is perceived as a weave and how it affects the eye as a motif or geometric repeat. If this sounds a little confusing it is because as I write I am not entirely sure I know what I am saying exactly either.

Examples of tessellations might be squares, rectangles, triangles, stars and other polygons. Of the polygons, the more sides you get to a polygon the harder it is to tessellate. For example, it is easy to make a rectangle tessellate into a herringbone formation or for that matter to make it into a whole bunch of tessellations which we might find commonly seen in parquet floors, or a quadrilateral which forms the basis of a chevron parquet floor. These more common shapes we find are expressed in silks each season too. Depending on the thickness and placement of these polygons you can change the handle and the appearance of the silk drastically. The smaller the shapes are the more it appears that you have changed the 'weave' when in actual fact the silk is woven in the same manner on say a satin warp.

Not since the 1970's has a new mathematical tessellation been derived for pentagons. They are a tricky lot to tessellate. The original tessellations had come from the German mathematician Karl Reinhardt in the early 1900's and then there was another wave in the 1950's through Marjorie Rice, a San Diego housewife. Recently, however, a new mathematical equation was derived for a tessellating pentagon and it was completed by Casey Mann, Jennifer McLoud and David Von Derau of the University of Washington Bothell.

I found the article in the The Guardian and immediately set about trying to turn this new pentagon into a silk. Whilst we were there we found another pentagon to tessellate and the results are very unique. No, they are not for everyone, but I envisage that the intellectual at an evening cocktail party would greatly benefit from one, something to begin a conversation with - about tessellations, about mathematics, about polygons or maybe just about about Christmas and the year that's passed.

Roughly 20 bows will be made from each silk. This is a limited edition silk.


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