Wednesday, November 5, 2014

Weaving bricks

A puck weaver of length 2 and corrugation frequency 3.
There is a "teleological" problem in polyphase unit weaving when the composite, polyphase weavers are shingled. Shingling effectively assigns to each composite weaver an orientation, i.e., the direction that the units "lean."As new crossing weavers are encountered in building up the basket surface, the entire basket would need to have been designed in advance in order to know which orientation to start them in.

Brick-laid unit weavers do not have an orientation, and thus escape this difficulty. Since all weavers form closed loops of even length, identical puck "bricks" that form these loops by being laid end-to-end  must have even length. In fact for the greatest versatility of shape they must have length two.

That leaves very little overlap for bricks in adjacent courses to engage one another, so higher frequency corrugation is useful for greater stiffness and frictional engagement between courses. The little puck "brick" pictured above begins to gain some inevitability.

In a single-layer course of these bricks laid end-to-end, spliced squares alternate with un-spliced squares. The un-spliced squares are the ones that the over-and-under pattern of kagome weaving will expose on that face. On the other face, the spliced squares of this course will be covered by the un-spliced squares of the other course.

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