Wednesday, December 31, 2014

Mesh resources of knotology weaving

Mesh resources of knotology weaving: the basket's folds and joins must lie along the edges of a mesh having up to four kinds of faces.
Knotology can realize a basket having a surface mesh composed of these four kinds of tiles: an isosceles right triangle, the squares of its side and hypotenuse, and an equilateral triangle with a side length matching that of the larger square.

The actual weavers are as wide as the smaller square and run parallel/perpendicular to the sides of the smaller square—and thus at 45° to the sides of the larger square. There is a fabric opening (hole) in the center of the larger square. Inside each equilateral triangle three weavers meet around a hole to form a cube corner that can be made either prominent (a peak) or recessed (a dell.)

More economically, the equilateral triangle is not needed, as the isosceles right triangle can build the capped triangles directly.

Still more economically, the right triangle alone suffices to build the smaller squares by joining hypotenuse to hypotenuse, and to build the larger squares by joining four together, side to side.

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