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== First Penrose Tiling/Original Pentagonal Tiling (P1) ==
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Penrose started his formation of different types of tiling with the first Penrose tiling, commonly abbreviated as P1. In 1619, Johannes Kepler, a notable astronomer, wrote in ''Harmonices Mundi'' that gaps in tiling that use regular polygons can only be filled with pentagrams, which are star polygons, decagons, and related shapes. As Penrose also observed, any attempt to tile a plane with regular pentagons will result in gaps. Penrose used Kepler's observation as inspiration, which leads to the types of shapes used in the first Penrose tiling: pentagons, stars (pentagrams), boats, and diamonds. Attached at the bottom of the page is an example of a first Penrose tiling, which can be used as a visual reference to any terms addressed. An example of a pentagon is shaded in red. An example of a star (pentagram) is shaded in orange. An example of a boat is shaded in green. A boat is essentially three-fifths of a star. An example of a diamond is shaded in purple. For the first Penrose tiling, there are a total set of six prototiles, which are essentially combinations of the different shapes that can be used without breaking the matching rules.
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Latest revision as of 01:05, 6 December 2020

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