So I have the following image of a shape X:
It's asking how to fill the plane with as much shape X as possible. I'm guessing it's asking me how to align it so that there is least amount of free space. Any way to figure that out?
2026-03-28 22:29:53.1774736993
The quadrilateral X has vertices at A = (0,1), B= (2,0), C=(6,1), and D= (6,4). How would you fill up the plane with the shape X as much as possible?
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Glue a mirrored copy of the quadrilateral along $AD$. You will obtain a convex hexagon which is symmetric with respect to the point $(3,5/2)$. This hexagon tessellates the plane (see LINK).
P.S. Any quadrilateral can tile the plane: http://demonstrations.wolfram.com/AnyQuadrilateralCanTile/