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Twisted bird base tessellation — molecule examples | by Michał Kosmulski
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Twisted bird base tessellation — molecule examples

I recently came up with the idea of the twisted bird base tessellation. As the name implies, it is based around the bird base which is folded with some extra paper and then twisted so that the flat part forms a square which enables tessellating. The central part pops out of the sheet and can be formed in many different ways. I plan to post a large version of the basic variant soon but in the meanwhile, here are some examples of how the molecules can be shaped.

 

These are obviously not all possibilities of shaping the molecules. Horizontally, the shaping of the four petals changes while the two vertical rows show two twisting directions of the central part.

 

Interestingly, each molecule in this example has three separate twists in three stacked layers, each with different properties:

- the lowest layer is the twist which enables tessellating the molecules: like in the plain square twist, two neighboring twists must have opposite chirality

- the middle layer is the stacking order of the four petals: this twist’s direction is independent from the twist below so you can have any twist direction that you like (many tessellations based around twists force a change in direction every other molecule); the middle variant is an exception since in order to thin the petals, layers have to be folded under the petal which is only possible if the rotation direction agrees with the twist that lies below

- finally, the third, upper-most twist is the middle part of the base: this twist’s direction is again independent from the direction of the twist below

 

Unlike many others, this tessellation is not based around a square or hexagonal grid.

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Taken on November 12, 2015