URL: Penrose Tiling

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https://en.wikipedia.org/wiki/Penrose_tiling

An example of aperiodic tiling, it does not contain arbitrarily large periodic regions or patches.

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Magic tile assembles organically, never creating a pattern

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This is the most complex shape known that can fit together organically, without a pattern (dubbed the Einstein tile, it was discovered by mathematicians in 2023). It has six sides of 1 unit length, six of 1÷1.73205080757 and one side measuring twice the latter. Placing the tiles is tricky because it is only logical to seek a pattern, but there is none. One method is to start with a center tile and move outward in a spiral, being ready to backtrack and place them upside down when a piece cannot be fit. The tile shape is a product of connecting four identical irregular pentagons - each made by cutting a regular hexagon into three pieces. To achieve the maximum precision, 3D print multiple cookie cutters and let them stiffen and shrink in the cutters. To round the upper corners use stretch wrap) when stamping (print cutters in both orientations if doing this). Tiling a floor or wall will present issues with the number of edge tiles that need to be cut. However, cutting at least some custom edge shapes is practical because only 90 and 120 degree angles are needed.

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