The fascinating tiling discovered by Sir Rogen Penrose in the middle 1970s may be constructed using the Generalized Dual Method, using an arrangement of lines. Let a set of equally-spaced parallel lines, one unit apart, be called a grid. Let a set of n non-zero, independent vectors be called a star. Let the star be the five unit vectors from center to vertices of a regular pentagon (of unit circumradious). Now create a grid perpendicular to each vector of the star, each grid centered upon the origin and containing one line passing through the origin. Now offset all five grids by 2/5, measured in the direction of each grid's star vector.
Above is an example of the resulting tiling. This strategy leads to a Penrose tiling with 5-fold symmetry governing the entire tiling. If the grids have inifnitely many lines, the entire plane is tiled. If the grids have an equal and finite number of lines, the Penrose tiling arises in a central region of a regular decagon tiled by 36- and 72-degree rhombs.
If the edges of the rhombs are suppressed, and the 36- and 72-degree rhombs colored differently, one obtains the effect seen above.
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