Tessellations

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Square Grids


Tessellating Star, made by Cyn of Wisconsin. Pattern from the book Tessellations by Jackie Robinson.



Isometric Grids



The isometric grid is made of 3 sets of parallel lines at 60 degrees to each other.
Several polygons tessellate on the isometric grid, including: (1) regular hexagon (2) 60 degree diamond (3) 30/30/120 degree triangle and (4) kite shape.

This Hoffman fabric purchased in June 1998 shows a tessellated pattern formed by tiling a 30/30/120 degree triangle over the plane.
You can change the pattern you see by focusing on the hexagons which tessellate in a "Baby's Block" pattern. Or, you can blend two adjacent skinny triangles together to make a 60 degree diamond, and focus on the diamond tessellation.

This fabric purchased in the early 1990s shows a tessellated pattern formed by tiling a clamshell shape at points on the isometric gric.

23 Hexagons from Quilts Every Day (QED) for Day 23 shows an example of regular hexagons on an isometric grid. However, these hexagons are not tessellating. The triangular spaces between the hexagons are called "frustrations." Do you suppose they're called that because the hexagons really, really want to tessellate?

Hexagon Pyramid from Quilts Every Day (QED) for Day 28 shows another example of regular hexagons on an isometric grid. In this example, they're tessellating.




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